Let width = w, then length = w + 20. The perimeter equals the fencing available: 2(w + w + 20) = 200. Simplifying: 2(2w + 20) = 200, so 4w + 40 = 200, thus 4w = 160, and w = 40 feet. The length = 40 + 20 = 60 feet. Area = 40 × 60 = 2400 square feet. Choice B results from using length = w + 10 instead of w + 20 (giving w = 45, l = 55, area = 2475, but this doesn't match either). Choice C comes from calculation errors. Choice D assumes incorrect perimeter equation.

First find the area for carpet: 15 × 12 = 180 square feet. Carpet cost: 180 × $4 = $720. Next find perimeter for baseboard: 2(15 + 12) = 2(27) = 54 feet. Baseboard cost: 54 × $2 = $108. Total cost: $720 + $108 = $828. Choice B only includes carpet cost. Choice C uses wrong area calculation (15 + 12 = 27, then 27 × 4 = 108 for carpet, plus 54 × 2 = 108 for trim, totaling 216, but this is incorrect math). Choice D uses area as perimeter (15 × 12 = 180, times $3 average cost).

For both rectangles, perimeter = 32, so 2(length + width) = 32, thus length + width = 16. Rectangle A: width = 6, so length = 16 - 6 = 10. Area A = 6 × 10 = 60 square meters. Rectangle B: width = 8, so length = 16 - 8 = 8. Area B = 8 × 8 = 64 square meters. Difference = 64 - 60 = 4 square meters. Choice A comes from finding the difference in widths (8 - 6 = 2) and doubling it. Choice B comes from finding the difference in lengths (10 - 8 = 2) and multiplying by width difference (2 × 8 = 16). Choice D comes from calculation errors.

This question tests 4th grade application of rectangle area and perimeter formulas to find missing dimensions (CCSS.4.MD.3). The area formula A = L × W means length times width equals area. To find a missing dimension when area is known, divide the area by the known dimension. For perimeter P = 2L + 2W, find the sum of both dimensions (P ÷ 2), then subtract the known dimension to find the unknown dimension. The rectangular classroom floor has an area of 96 square feet and a length of 12 feet, requiring students to find the width. Choice A is correct because dividing the area by the known length gives the width: 96 ÷ 12 = 8 feet, demonstrating understanding the formula as a multiplication equation with an unknown factor. Choice C represents multiplying instead of dividing (12 × 9 = 108, perhaps confusing with perimeter), which happens when students don't recognize the area formula requires division to solve backwards. To help students: Use area models with grid paper to show L × W = A visually, demonstrating that if you know A and L, you can find W by dividing. For perimeter, draw rectangles and label all four sides to show why the formula is 2L + 2W. Have students write out the formula with known values plugged in, then solve for the unknown. Watch for: students who multiply when they should divide, students who forget to divide perimeter by 2 before subtracting, and students who confuse area (square units) with perimeter (linear units).

This question tests 4th grade application of rectangle area and perimeter formulas to find missing dimensions (CCSS.4.MD.3). The area formula A = L × W means length times width equals area. To find a missing dimension when area is known, divide the area by the known dimension. For perimeter P = 2L + 2W, find the sum of both dimensions (P ÷ 2), then subtract the known dimension to find the unknown dimension. The rectangular garden bed has a perimeter of 48 feet and a width of 10 feet, requiring students to find the length. Choice A is correct because half the perimeter minus known width gives length: (48 ÷ 2) - 10 = 14 feet, demonstrating understanding the formula as an equation to solve for the unknown. Choice B represents not dividing by 2 first: 48 - 2×10 = 28, then perhaps misapplying, which happens when students forget both dimensions appear twice in perimeter. To help students: For perimeter, draw rectangles and label all four sides to show why the formula is 2L + 2W. Have students write out the formula with known values plugged in, then solve for the unknown. Watch for: students who forget to divide perimeter by 2 before subtracting, and students who confuse area (square units) with perimeter (linear units).

This question tests 4th grade application of rectangle area and perimeter formulas to find missing dimensions (CCSS.4.MD.3). The area formula A = L × W means length times width equals area. To find a missing dimension when area is known, divide the area by the known dimension. For perimeter P = 2L + 2W, find the sum of both dimensions (P ÷ 2), then subtract the known dimension to find the unknown dimension. The rectangular rug has an area of 60 square meters and a length of 12 meters, requiring students to find the width. Choice B is correct because dividing the area by the known length gives the width: 60 ÷ 12 = 5 meters, demonstrating understanding the formula as a multiplication equation with an unknown factor. Choice A represents multiplying instead of dividing (12 × 4 = 48, perhaps misapplying factors), which happens when students don't recognize the area formula requires division to solve backwards. To help students: Use area models with grid paper to show L × W = A visually, demonstrating that if you know A and L, you can find W by dividing. For perimeter, draw rectangles and label all four sides to show why the formula is 2L + 2W. Have students write out the formula with known values plugged in, then solve for the unknown. Watch for: students who multiply when they should divide, students who forget to divide perimeter by 2 before subtracting, and students who confuse area (square units) with perimeter (linear units).

This question tests 4th grade application of rectangle area and perimeter formulas to find missing dimensions (CCSS.4.MD.3). The area formula A = L × W means length times width equals area. To find a missing dimension when area is known, divide the area by the known dimension. For perimeter P = 2L + 2W, find the sum of both dimensions (P ÷ 2), then subtract the known dimension to find the unknown dimension. The rectangular yard has a perimeter of 56 feet and a length of 18 feet, requiring students to find the width. Choice A is correct because half the perimeter minus known length gives width: (56 ÷ 2) - 18 = 10 feet, demonstrating understanding the formula as an equation to solve for the unknown. Choice B represents not subtracting correctly: 56 ÷ 2 = 28, which happens when students forget to subtract the known dimension after dividing. To help students: For perimeter, draw rectangles and label all four sides to show why the formula is 2L + 2W. Have students write out the formula with known values plugged in, then solve for the unknown. Watch for: students who forget to divide perimeter by 2 before subtracting, and students who confuse area (square units) with perimeter (linear units).

This question tests 4th grade application of rectangle area and perimeter formulas to find missing dimensions (CCSS.4.MD.3). The area formula A = L × W means length times width equals area. To find a missing dimension when area is known, divide the area by the known dimension. For perimeter P = 2L + 2W, find the sum of both dimensions (P ÷ 2), then subtract the known dimension to find the unknown dimension. The rectangular poster board has an area of 120 square inches and a width of 8 inches, requiring students to find the length. Choice A is correct because dividing the area by the known width gives the length: 120 ÷ 8 = 15 inches, demonstrating understanding the formula as a multiplication equation with an unknown factor. Choice B represents multiplying instead of dividing (8 × 14 = 112, perhaps confusing factors), which happens when students don't recognize the area formula requires division to solve backwards. To help students: Use area models with grid paper to show L × W = A visually, demonstrating that if you know A and L, you can find W by dividing. For perimeter, draw rectangles and label all four sides to show why the formula is 2L + 2W. Have students write out the formula with known values plugged in, then solve for the unknown. Watch for: students who multiply when they should divide, students who forget to divide perimeter by 2 before subtracting, and students who confuse area (square units) with perimeter (linear units).

This question tests 4th grade application of rectangle area and perimeter formulas to find missing dimensions (CCSS.4.MD.3). The area formula A = L × W means length times width equals area. To find a missing dimension when area is known, divide the area by the known dimension. For perimeter P = 2L + 2W, find the sum of both dimensions (P ÷ 2), then subtract the known dimension to find the unknown dimension. The rectangular floor is covered with 48 tiles arranged in 6 rows, requiring students to find the number of tiles per row using the area idea. Choice B is correct because dividing the total tiles by the number of rows gives tiles per row: 48 ÷ 6 = 8 tiles, demonstrating understanding the formula as a multiplication equation with an unknown factor. Choice C represents multiplying instead of dividing (6 × 7 = 42, perhaps confusing factors), which happens when students don't recognize the area formula requires division to solve backwards. To help students: Use area models with grid paper to show L × W = A visually, demonstrating that if you know A and L, you can find W by dividing. For perimeter, draw rectangles and label all four sides to show why the formula is 2L + 2W. Have students write out the formula with known values plugged in, then solve for the unknown. Watch for: students who multiply when they should divide, students who forget to divide perimeter by 2 before subtracting, and students who confuse area (square units) with perimeter (linear units).

This question tests 4th grade application of rectangle area and perimeter formulas to find missing dimensions (CCSS.4.MD.3). The area formula A = L × W means length times width equals area. To find a missing dimension when area is known, divide the area by the known dimension. For perimeter P = 2L + 2W, find the sum of both dimensions (P ÷ 2), then subtract the known dimension to find the unknown dimension. The rectangular yard has a perimeter of 48 feet and a width of 10 feet, requiring students to find the length. Choice A is correct because half the perimeter minus the known width gives the length: (48 ÷ 2) - 10 = 14 feet, demonstrating understanding the formula as an equation to solve for the unknown. Choice C represents adding the perimeter and width without dividing (48 - 10 = 38, perhaps forgetting to halve first), which happens when students forget both dimensions appear twice in perimeter. To help students: Use area models with grid paper to show L × W = A visually, demonstrating that if you know A and L, you can find W by dividing. For perimeter, draw rectangles and label all four sides to show why the formula is 2L + 2W. Have students write out the formula with known values plugged in, then solve for the unknown. Watch for: students who multiply when they should divide, students who forget to divide perimeter by 2 before subtracting, and students who confuse area (square units) with perimeter (linear units).