Question

The perimeter of a rhombus is 100 m and one of its diagonals is 40 m. Find its other diagonal and area.

Answer 1

Given: Perimeter = 100 m, one diagonal d₁ = 40 m.

Step-wise calculation:

1. Side length `s = "Perimeter"/4`

= `100/4`

= 25 m

2. Diagonals of a rhombus bisect each other at right angles, so in the right triangle formed by half-diagonals:

`(d_1/2)^2 + (d_2/2)^2 = s^2`

Substitute values:

`(40/2)^2 + (d_2/2)^2 = 25^2`

⇒ `20^2 + (d_2/2)^2 = 625`

⇒ `400 + (d_2/2)^2 = 625`

⇒ `(d_2/2)^2 = 225`

⇒ `d_2/2 = 15`

⇒ d₂ = 30 m

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

= `(40 xx 30)/2`

= 600 m²

Other diagonal = 30 m; Area = 600 m².