Asked by sanjna

the perimetre of the rohmbus is 52cm and one of its diagnol is 10 cm find the length of the other diognol and the area of the rohmbus

Answers

Answered by drwls
Since a rhombus has four equal side lengths, the side length is
s = 52/4 = 13 cm.

If one diagonal is d1 = 10 cm long, the half-diagonal is 5 cm and the other (longer) half-diagonal is
d2/2 = sqrt(a^2 - 5^2) = 12 cm, so the other diagonal length is
d2 = 24 cm. I could use the Pythagorean Theorem because the two intersecting diagonals or a rhombus form four right angle triangles with the sides.

The area is (1/2)d1*d2 = (1/2)*10*24
= 120 cm^2
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