Question

The perimeter of a rhombus is 52 cm. The length of one diagonal of the rumpus is 24 cm. What is the length of the other diagonal?

Answer 1

10 cm

Explanation:

Each side = 52/2 = 13

Angle 1: X

24² = 13² + 13² - 2(13)(13)cosX

X = 134.7602701

Angle 2: 180 - X = 45.2397299

Diagonal² = 13² + 13² - 2(13)(13)cos(180-X)

Diagonal² = 100

Diagonal = 10

Answer 2

The perimeter of a rhombus is 52 cm.

=> length of side: L = 52/4 = 13 cm

Applying Pythagorean theorem for a particular right triangle inside rhombus, we have:

diagonal_2 = 2 x sqrt(side^2 - (diagonal_1/2)^2)

= 2 x sqrt(13^2 - (24/2)^2)

= 2 x 5 = 10 (cm)

=> Solution : 10 cm

Hope this helps!

:)