2 steps to this problem.
1) Figure out the length of the sides. The perimeter is:
2L + 2W
We know that the width is [tex]\frac{3}{4} [/tex] of the length, so we can rewrite this to be
2L + 2([tex]\frac{3}{4} [/tex])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.
[tex] a^{2} + b^{2} = c^{2} [/tex]
-->
[tex] 20^{2} + 15^{2} = c^{2} [/tex]
-->
[tex] \sqrt{20^{2} + 15^{2}}[/tex] = diagonal length = 25
