Question

the perimeter of a rectangle is 70 inches. the ratio of the length to width is 4:3. find the length of the diagonal of the rectangle.

Answer 1

2 steps to this problem.

1) Figure out the length of the sides. The perimeter is:

2L + 2W

We know that the width is
`(3)/(4)` of the length, so we can rewrite this to be

2L + 2(
`(3)/(4)`)W

or in other words,

3.5L = 70
-->
L = 20
-->
W = 15

2. Figure out the length of the diagonal. The shape is a right triangle, so you can use the Pythagorean Theorem here.


`a^(2) + b^(2) = c^(2)`
-->

`20^(2) + 15^(2) = c^(2)`
-->

`\sqrt{20^(2) + 15^(2)}` = diagonal length = 25