Question

The area of a rhombus is 120 m². If one of the diagonals is 24 m, find the perimeter of the rhombus.

Answer 1

Given:

Area A = 120 m²

One diagonal d₁ = 24 m

Step-wise calculation:

1. Use area formula for a rhombus:

`A = (d_1 xx d_2)/2`

2. Solve for the other diagonal d₂:

`d_2 = (2A)/(d_1)`

= `(2(120))/24`

= `240/24`

= 10 m

3. The diagonals bisect each other at right angles, so half-diagonals are 12 m and 5 m.

4. Find the side length (by Pythagoras in one right triangle formed by half-diagonals):

Side = `sqrt(12^2 + 5^2)`

= `sqrt(144 + 25)`

= `sqrt(169)`

= 13 m

5. Perimeter = 4 × side

= 4 × 13

= 52 m

The perimeter of the rhombus is 52 m.