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If sum of diagonals of a rhombus is 10 cm and its area is \( \Large 12 cm^{2} \), then lengths of its diagonals are

A) 5, 5
B) 9, 1
C) 8, 2
D) 6, 4

Correct Answer:




D) 6, 4

Description for Correct answer:

Since diagonals of rhombus bisect each other at \( \Large 90 ^{\circ} \),

Therefore, \( \Large 2x + 2y = 10 \)

\( \Large x + y = 5 \) ... (i)

\( \Large Area \ of \ ABCD = 4 \times \triangle ABCD \)
Area ABCD = \( \Large 4 \times \left(\frac{1}{2} \times AP \times PD\right) \)

=\( \Large 2xy \)

Therefore, \( \Large 2xy = 12 \)

=> \( \Large xy = 6 \) .. (ii)

Solving equations (i) and (ii), we get

x = 3 and y = 2

Hence diagonals are 6 cm and 4 cm.

Part of solved Quadrilateral and parallelogram questions and answers : >> Elementary Mathematics >> Quadrilateral and parallelogram

Comments

Similar Questions

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