Question

If the perimeter of A is 36 ft and the perimeter of B is 48 ft, what is the perimeter of C. If the area of C is 400 f12 and the perimeter of B is 64 ft, what is the side length of square A? B square C? G

Answer 1

If the perimeter of A is 36 ft and the perimeter of B is 48 ft, what is the perimeter of C?

In the image , the sides of A, B and C makes up a right triangle , where C is the hypotenuse

To solve for C, we may use the pythagorean theorem

`C=\sqrt[]{A^2+B^2}`

where A and B are the sides of Box A and B

If the perimeter of Box A = 36 ft, then the length of the sides of box A = 36/4 = 9 ft

If the perimeter of Box B = 48 ft, then the length of the sides of box B = 48/4 = 12 ft

Using the pythagorean theorem , we can solve for the length of the sides

of box C

`\begin{gathered} C=\sqrt[]{A^2+B^2} \\ C=\sqrt[]{9^2+12^2} \\ C=\sqrt[]{81+144} \\ C=\sqrt[]{225} \\ C=15 \end{gathered}`

If the side of box C is 15, then the perimeter of box C is = 15 x 4 = 60 ft

If the area of C is 400 f12 and the perimeter of B is 64 ft, what is the side length of square A?

If the area of box C is 400 sq. ft., then the length of the side of box C is = (400)^1/2 = 20 ft

If the perimeter of box B is 64 ft, then the length ofthe sides of box B is = 64/4 = 16 ft.

Using the pythagorean theorem , we can solve for the length of the side of box C

`\begin{gathered} A=\sqrt[]{C^2-B^2} \\ A=\sqrt[]{20^2-16^2} \\ A=\sqrt[]{400-256} \\ A=\sqrt[]{144} \\ A=12 \end{gathered}`

The length of the sides of box A is 12 ft

Answers:

The perimeter of box C is 60 ft

The length of the sides of box A is 12 ft