Question

The perimeter of a rhombus is 100 cm. Its one diagonal is 48 cm. Its area is ______.

Options

• 336 cm²

• 168 cm²

• 196 cm²

• 720 cm²

Answer 1

The perimeter of a rhombus is 100 cm. Its one diagonal is 48 cm. Its area is 336 cm².

Explanation:

Given the perimeter of the rhombus is 100 cm, each side is:

Side = `"Perimeter"/4`

= `100/4`

= 25 cm

One diagonal d₁ = 48 cm is given.

The diagonals of a rhombus bisect each other at right angles, so half of the given diagonal is 24 cm.

Let the other diagonal be d₂.

Then half of d₂ is x.

Using the right triangle formed by half the diagonals and the side:

x² + 24² = 25²

x² + 576 = 625

x² = 625 – 576

x² = 49

x = 7 cm

So, the other diagonal d₂ = 2 × 7 = 14 cm.

Now, the area (A) of the rhombus is given by half the product of the diagonals:

`A = 1/2 xx d_1 xx d_2`

= `1/2 xx 48 xx 14`

= 24 × 14

= 336 cm²

Thus, the area is 336 cm².