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,
[tex]AD^2=AE^2 +ED^2[/tex]
[tex]AD^2=15^2 +20^2[/tex]
[tex]AD^2=225+400[/tex]
[tex]AD^2=625[/tex]
[tex]AD^2=25^2[/tex]
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.
