The perimeter of a rectangle is simply the sum of the four sides:

\(\displaystyle 1000+1000+100+100=2200\; meters\)

We know that:

\(\displaystyle Perimeter=2(a+b)\)

where:

\(\displaystyle a=Length \ of\ the\ rectangle\)

\(\displaystyle b= Width\ of\ the\ rectangle\)

So we can write:

\(\displaystyle 64=2(10x+6x)\Rightarrow 10x+6x=32\Rightarrow 16x=32\Rightarrow x=2\)

To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.

\(\displaystyle P=9+4+9+4=26\: in\)

The perimeter of the parallelogram is the sum of the four side lengths - here, that formula becomes

\(\displaystyle P = a + b + a + b = 18 + 26 + 18 + 26 = 88\).

Note that the height \(\displaystyle h\) is irrelevant to the answer.

The formula for the perimeter of a rectangle is \(\displaystyle \dpi{100} Perimeter=2l+2w\).

Plug in our given values to solve:

\(\displaystyle \dpi{100} Perimeter = 2(20)+2(3)\)

\(\displaystyle \dpi{100} Perimeter = 20+6\)

\(\displaystyle \dpi{100} Perimeter = 26\)

The trick here is that we don't know which is the repeated side. Our possible triangles are therefore 20 + 20 + 30 = 70 or 30 + 30 + 20 = 80.  The difference is therefore 80 – 70 or 10.

There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.

The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by

180 = 30+2x → x = 75°

We can use ratios to find the unknown side:

75/5 = 30/y → 75y = 150 → y = 2''.

Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.

To inscribe means to draw inside a figure so as to touch in as many places as possible without overlapping. The circle is inside the square such that the diameter of the circle is the same as the side of the square, so the side is actually 4 in.  The perimeter of the square = 4s = 4 * 4 = 16 in.

Find the area of Square Y, then calculate the area of Square X.

If the perimeter of Square Y is 24, then each side is 24/4, or 6.

A = 6 * 6 = 36 sq ft, for Square Y

If Square X has 3 times the area, then 3 * 36 = 108 sq ft.

The area of the given square is given by \(\displaystyle A = s^{2}\) so the side must be 6 in.  The side is reduced by a factor of two, so the new side is 3 in.  The perimeter of the new square is given by \(\displaystyle P = 4s = 4\cdot 3 = 12 in\).