Question

the perimeter of rhombus is 180 cm and one of its diagonal is 72 cm find the length of the Other diagonal and the area of rhombus

Answer 1

HEY DEAR ...

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.

HOPE , IT HELPS ...