Question

Freshman geometry!!! number for please help!!

Answer 1

Option C:

The perimeter of the rhombus is 100 inches.

Solution:

AC = 30 inches, BD = 40 inches

In rhombus, diagonals bisect each other at right angles.

AE = CE = 15 inches

BE = ED = 20 inches

In ΔAED, ∠E = 90°

Using Pythagorean theorem,

$AD^2=AE^2 +ED^2$

$AD^2=15^2 +20^2$

$AD^2=225+400$

$AD^2=625$

$AD^2=25^2$

Taking square root on both sides, we get

AD = 25 inches

In rhombus, all sides are equal in length.

AD = DC = CB = BA = 25 inches.

Perimeter = AD + DC + CB + BA

                 = 25 + 25 + 25 + 25

                 = 100 inches

The perimeter of the rhombus is 100 inches.

Option C is the correct answer.