Question

the perimeter of rhombus is 20cm. one diognal of rhombus is 8cm. find the other diognal of rhombus

Answer 1

Given, Perimeter of a rhombus = 20 cm
Perimeter of a rhombus = 4*side
Hence, side = 20/4 = 5 cm.
Now, we know that the diagonals of a rhombus bisect each other at right angles (90 degree).
Hence 'a right angled triangle can be visualised with 'side' as the hypotenuse'.

diagonal length = 8 cm
Half the length (since diagonal bisects each other) = 8/2 = 4 cm
(d/2)^2 + (d1/2)^2 = 5^2
4^2 + (d1/2)^2 = 5^2
(d1/2)^2 = 9
d1/2 = 3
d1 = 3*2 = 6 cm
Hence other diagonal = 6 cm.

Area = 1/2 * d1*d = 1/2 * 8 * 6 = 24 cm^2
Hope it helps. 

R