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

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

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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.

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