Question

Given:• EFGH is a rhombus• The perimeter of EFGH is 32m70HWhich is closest to the length of EG?5.50 7.51516

Answer 1

Take into account that the each side of the rhombus has the same length, then, each side has the following length:

$\text{s}=\frac{32}{4}=8$

moreover, consider that segment EG is one diagonal of the rhombus, then, use the following formula to get the length of EG:

$EG=s\sqrt[]{2+2\cos \theta}$

where θ = 70.

Replace the values of θ and s into the expression fro EG:

$EG=8\sqrt[]{2+2\cos 70}=13.10$

by comparing with the given answer choices, you can conclude that the closest length is 15.