Rhombus ABCD has perimeter 148, and one of its diagonals has length 24. How long is the other diagonal?

FluffyDinosaur
Jun 30, 2018

#1**0 **

By definition: 148/4 =37 - measure of one side.

By Pythagoras's Theorem:

24/2 =12 half of the given diagonal

37^2 - 12^2 =D^2, where D =1/2 of the 2nd diagonal

1,369 - 144 =D^2

1,225 =D^2

D =sqrt(1,225)

D =35 - This is 1/2 of the 2nd diagonal

35 x 2 = 70 - measure of the 2nd diagonal.

Guest Jun 30, 2018