ISEE Middle Level Quantitative : Plane Geometry

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

Example Question #101 : Plane Geometry

What is the length of a rectangular room with an area of \(\displaystyle 99ft^2\) and a width of \(\displaystyle 9ft?\)

 

Possible Answers:

\(\displaystyle 11ft\)

\(\displaystyle 8ft\)

\(\displaystyle 10ft\)

\(\displaystyle 9ft\)

\(\displaystyle 7ft\)

Correct answer:

\(\displaystyle 11ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 99=l\times 9\)

\(\displaystyle \frac{99}{9}=\frac{l\times 9}{9}\)

\(\displaystyle 11=l\)

Example Question #102 : Solve Problems Involving Measurement And Conversion Of Measurements

What is the length of a rectangular room with an area of \(\displaystyle 72ft^2\) and a width of \(\displaystyle 8ft?\)

 

Possible Answers:

\(\displaystyle 10ft\)

\(\displaystyle 9ft\)

\(\displaystyle 12ft\)

\(\displaystyle 13ft\)

\(\displaystyle 11ft\)

Correct answer:

\(\displaystyle 9ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 72=l\times 8\)

\(\displaystyle \frac{72}{8}=\frac{l\times 8}{8}\)

\(\displaystyle 9=l\)

Example Question #102 : Plane Geometry

What is the length of a rectangular room with an area of \(\displaystyle 80ft^2\) and a width of \(\displaystyle 8ft?\)

 

Possible Answers:

\(\displaystyle 10ft\)

\(\displaystyle 8ft\)

\(\displaystyle 7ft\)

\(\displaystyle 6ft\)

\(\displaystyle 9ft\)

Correct answer:

\(\displaystyle 10ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 80=l\times 8\)

\(\displaystyle \frac{80}{8}=\frac{l\times 8}{8}\)

\(\displaystyle 10=l\)

Example Question #77 : Parallelograms

What is the length of a rectangular room with an area of \(\displaystyle 42ft^2\) and a width of \(\displaystyle 7ft?\)

 

Possible Answers:

\(\displaystyle 7ft\)

\(\displaystyle 6ft\)

\(\displaystyle 4ft\)

\(\displaystyle 8ft\)

\(\displaystyle 5ft\)

Correct answer:

\(\displaystyle 6ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 42=l\times 7\)

\(\displaystyle \frac{42}{7}=\frac{l\times 7}{7}\)

\(\displaystyle 6=l\)

Example Question #21 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

What is the length of a rectangular room with an area of \(\displaystyle 49ft^2\) and a width of \(\displaystyle 7ft?\)

 

Possible Answers:

\(\displaystyle 4ft\)

\(\displaystyle 8ft\)

\(\displaystyle 7ft\)

\(\displaystyle 6ft\)

\(\displaystyle 5ft\)

Correct answer:

\(\displaystyle 7ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 49=l\times 7\)

\(\displaystyle \frac{49}{7}=\frac{l\times 7}{7}\)

\(\displaystyle 7=l\)

Example Question #79 : Parallelograms

What is the length of a rectangular room with an area of \(\displaystyle 60ft^2\) and a width of \(\displaystyle 12ft?\)

 

Possible Answers:

\(\displaystyle 7ft\)

\(\displaystyle 4ft\)

\(\displaystyle 6ft\)

\(\displaystyle 5ft\)

\(\displaystyle 8ft\)

Correct answer:

\(\displaystyle 5ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 60=l\times 12\)

\(\displaystyle \frac{60}{12}=\frac{l\times 12}{12}\)

\(\displaystyle 5=l\)

Example Question #80 : Parallelograms

What is the length of a rectangular room with an area of \(\displaystyle 63ft^2\) and a width of \(\displaystyle 7ft?\)

 

Possible Answers:

\(\displaystyle 4ft\)

\(\displaystyle 8ft\)

\(\displaystyle 9ft\)

\(\displaystyle 7ft\)

\(\displaystyle 5ft\)

Correct answer:

\(\displaystyle 9ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 63=l\times 7\)

\(\displaystyle \frac{63}{7}=\frac{l\times 7}{7}\)

\(\displaystyle 9=l\)

Example Question #135 : How To Find The Area Of A Rectangle

What is the length of a rectangular room with an area of \(\displaystyle 55ft^2\) and a width of \(\displaystyle 11ft?\)

Possible Answers:

\(\displaystyle 6ft\)

\(\displaystyle 8ft\)

\(\displaystyle 5ft\)

\(\displaystyle 9ft\)

\(\displaystyle 7ft\)

Correct answer:

\(\displaystyle 5ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 55=l\times 11\)

\(\displaystyle \frac{55}{11}=\frac{l\times 11}{11}\)

\(\displaystyle 5=l\)

Example Question #202 : Plane Geometry

What is the length of a rectangular room with an area of \(\displaystyle 70ft^2\) and a width of \(\displaystyle 7ft?\)

 

Possible Answers:

\(\displaystyle 13ft\)

\(\displaystyle 10ft\)

\(\displaystyle 11ft\)

\(\displaystyle 9ft\)

\(\displaystyle 12ft\)

Correct answer:

\(\displaystyle 10ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 70=l\times 7\)

\(\displaystyle \frac{70}{7}=\frac{l\times 7}{7}\)

\(\displaystyle 10=l\)

Example Question #203 : Plane Geometry

What is the length of a rectangular room with an area of \(\displaystyle 48ft^2\) and a width of \(\displaystyle 6ft?\)

 

Possible Answers:

\(\displaystyle 7ft\)

\(\displaystyle 10ft\)

\(\displaystyle 6ft\)

\(\displaystyle 8ft\)

\(\displaystyle 9ft\)

Correct answer:

\(\displaystyle 8ft\)

Explanation:

\(\displaystyle A=l\times w\)

We have the area and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 48=l\times 6\)

\(\displaystyle \frac{48}{6}=\frac{l\times 6}{6}\)

\(\displaystyle 8=l\)

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