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XAT 2018 — QA & DI Question 3

Basics of QuadrilateralsEasy

If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find the area of the rhombus.

Answer & solution

  • A

    54 sq. cm.

  • B

    108 sq. cm.

  • C

    144 sq. cm.

  • D

    200 sq. cm.

  • None of the above

Solution

We know that the diagonals of a rhombus bisect each other at right angles.

So, let’s assume that the two diagonals have lengths 6x and 8x.

​​​​​​​

⇒ (3x)2 + (4x)2 = 152

⇒ 25x2 = 225

⇒ x2 = 9

⇒ x = 3

∴ The length of the diagonals are 18 and 24.

∴ Area of the rhombus = ½ × product of the diagonals = ½ × 18 × 24 = 216

Hence, option (e).

XAT 2018 QA & DI Q3: If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find the area of the rhombus. — Solution | TheCATExam