CUET PG 2023 — Reasoning PYQ

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Question

CUET PG 2023 — Reasoning PYQ

CUET PG | Reasoning | 2023

The area of a rhombus is 120 cm2 and length of its one diagonal in 24 cm. Find the perimeter of the rhombus (in cm).

Choose the correct answer:

Explanation

Step 1: Find the length of the second diagonal ( $d_2$ )

The area of a rhombus is given by the formula:

\text{Area} = \frac{1}{2} \times d_1 \times d_2

Given:

$\text{Area} = 120\text{ cm}^2$
$d_1 = 24\text{ cm}$

Substituting the values:

120 = \frac{1}{2} \times 24 \times d_2

120 = 12 \times d_2

d_2 = \frac{120}{12} = 10\text{ cm}

Step 2: Find the side of the rhombus ( $a$ )

The diagonals of a rhombus bisect each other at right angles ( $90^\circ$ ). This creates four right-angled triangles inside the rhombus. The side ( $a$ ) can be found using the Pythagorean theorem:

a = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2}

Substituting $d_1 = 24$ and $d_2 = 10$ :

a = \sqrt{\left(\frac{24}{2}\right)^2 + \left(\frac{10}{2}\right)^2}

a = \sqrt{12^2 + 5^2}

a = \sqrt{144 + 25}

a = \sqrt{169} = 13\text{ cm}

Step 3: Find the perimeter

The perimeter ( $P$ ) of a rhombus is four times its side length:

P = 4 \times a

P = 4 \times 13 = 52\text{ cm}

Final Answer

The perimeter of the rhombus is $52\text{ cm}$ .