Question

if the perimeter of a rhombus is 80 cm and one of its diagonal is 24 cm then find the length of the Other diagonal

Answer 1

32 will be the answer

Answer 2

Given - Perimeter and diagonal

Find - Length of other diagonal

Solution - Length of other diagonal = 32 centimetres.

Perimeter of rhombus = 4*side

80 = 4*side

Side = 20 centimetres

Now, taking one triangle formed by one side of rhombus and half of two diagonals. The length of one diagonal will be taken as 12 centimetres and the other diagonal will be taken as x centimetres.

So, using Pythagoras theorem to find the value of x.

side² = (known diagonal)² + (other diagonal)²

20² = 12² + (other diagonal)²

(other diagonal)² = 400 - 144

(other diagonal)² = 256

(other diagonal) = 16 centimetres.

Thus, the length of other diagonal will be 16 + 16

Length of other diagonal = 32 centimetres.