Question

The perimeter of a rhombus is 180 cm and one of its diagonals is 72 cm. Find the length of the other diagonal and the area of the rhombus

Answer 1

let


a = the wide of the rhombus

d1 = 72cm the diagonal of the rhombus

d2 = the other diagonal of the rhombus


the perimeter of a rhombus is 180 cm


4a = 180 => a = 180/4 


a = 45 cm


the diagonals d1 and d2 of a rhombus bisect each other at right angles. using the Pythagorean Theorem we have


(d1/2)^2 + (d2/2)^2 = a^2


(72/2)^2 + (d2/2)^2 = 45^2


36^2 + (d2/2)^2 = 2025


by solving the equation we find and consider only the positive roots


d2 = 54 cm

the are of the rhombus is A = (d1*d2)/2


A = 72*54/2


A = 1944 cm^2


thus ,
the length of the other diagonal of the rhombus is 54 cm.

the area of the rhombus is 1944 cm^2.