Question:
PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=\(4\sqrt{x}\) cm then the length of each side of the rhombus (in terms of ‘x’) is:
PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=\(4\sqrt{x}\) cm then the length of each side of the rhombus (in terms of ‘x’) is:
Updated On: Sep 13, 2024
- \((\sqrt{x }+ 18) cm\)
- \(5\sqrt{x}\, cm\)
- 18 cm
- 30 cm
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The Correct Option is D
Solution and Explanation
The correct option is (D): 30 cm.
According to the question,
PQ = 30 cm, PR = 36 cm and QS = \(4\sqrt{x}\) cm
Therefore, OP = \(\frac{36}{2}\) = 18 cm and OQ = \(\frac{4\sqrt{x}}{2} \)= \(2\sqrt{x}\) cm (Since diagonals of rhombus bisect each other at right angle)
In triangle POQ, using Pythagoras theorem
182 + (\(2\sqrt{x}\))2 = 302
Or, 324 + 4x = 900
Or, 4x = 576
Or, x = 144
Therefore, length of each side of the rhombus = \(\sqrt{x}\)+18=12+18=30 cm.
According to the question,
PQ = 30 cm, PR = 36 cm and QS = \(4\sqrt{x}\) cm
Therefore, OP = \(\frac{36}{2}\) = 18 cm and OQ = \(\frac{4\sqrt{x}}{2} \)= \(2\sqrt{x}\) cm (Since diagonals of rhombus bisect each other at right angle)
In triangle POQ, using Pythagoras theorem
182 + (\(2\sqrt{x}\))2 = 302
Or, 324 + 4x = 900
Or, 4x = 576
Or, x = 144
Therefore, length of each side of the rhombus = \(\sqrt{x}\)+18=12+18=30 cm.
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