Question

The perimeter of a rhombus is 20 cm. If one diagonal of the rhombus is 8 cm, find

1. the length of the other diagonal,
2. the area of the rhombus.

Answer 1

Given:

Perimeter = 20 cm, so each side a = `20/4` = 5 cm.

One diagonal d₁ = 8 cm.

Step-wise calculation:

1. In a rhombus the diagonals bisect each other at right angles, so halves of the diagonals and a side form a right triangle.

2. Let the other diagonal be d₂.

Then `(d_1/2)^2 + (d_2/2)^2 = a^2`.

`(8/2)^2 + (d_2/2)^2 = 5^2`

`4^2 + (d_2/2)^2 = 25`

`16 + (d_2^2)/4 = 25`

`(d_2^2)/4 = 9`

⇒ `d_2^2 = 36`

⇒ d₂ = 6 cm

3. Area of a rhombus = `(d_1 xx d_2)/2`.

Area = `(8 xx 6)/2`

= 24 cm²

i. Other diagonal = 6 cm.

ii. Area = 24 cm².