Question

The diagonal of a rhombus is 25% less than the other diagonal. The area of the rhombus is 24 cm². What is the length of the side of the rhombus?

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer:

C. 5

Solution:

Given:

Area of Rhombus = 24 cm

The one diagonal of the Rhombus is 25% less than other.

Calculation:

Let the length of side of Rhombus be AB = BC = CD = DA = a

As we know,

⇒ Area of the Rhombus = $\frac{1}{2}$ $\times$ {d₁} $\times$ {d₂}

⇒ Let Length of the one diagonal d₁= 4x

∴ Length of the other diagonal d₂=25% less than d₁

$= 4x\times{\frac{75}{100}}$

d₂$=4x\times{\frac{3}{4}}$ = 3x

According to the question,

$⇒\frac{1}{2}\times{4x}\times{3x} = 24$

⇒ x = 2

Length of the diagonal of the rhombus $= 4x = 4\times{2} = 8$

⇒ Length of the other diagonal of the rhombus $= 3x = 3 \times{2} = 6$

As we know,

⇒ a² = 4² + 3² = 25

⇒ a = 5