
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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