Question

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

Answer 1

Answer:

diagonal is 54 and area is 1944

Step-by-step explanation:

1. given, perimeter of rhombus=180 so one is 45 because all sides are equal and given diagonal is 72 take a right angle triangle in rhombus it will have one side with length 36 ( half of diagonal) because diagonals in rhombus bisect each other now taking that right angle triangle find its another side with Pythagoras thearom and double the side to get another diagonal (54) and use 1/2× diagonal 1×diagonal2

Answer 2

Step-by-step explanation:

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

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

the area of the rhombus is 1944 cm^2.