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

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