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Standard VIII

Mathematics

Rhombus

The diagonals...

Question

The diagonals of rhombus PQRS intersect at O. If PQ = 20 cm diagonal PR = 28 cm. Find length of SQ.

\sqrt{204}

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204

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2 \sqrt{204}

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408

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Solution

The correct option is B $2 \sqrt{204}$ cm
Diagonals of rhombus bisect each other.
All sides of a rhombus are congruent.

$∴ O S = O Q$

In $△ R O Q, O Q = \sqrt{20^{2} - 14^{2}}$ ...... By Pythagoras theorem

$O Q = \sqrt{400 - 146}$

$O Q = \sqrt{204}$

$S Q = 2 \sqrt{204}$ cm .... (S-O-Q)

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The diagonals of rhombus PQRS intersect at O. If PQ = 20 cm diagonal PR = 28 cm. Find length of SQ.

The correct option is B 2√204 cmDiagonals of rhombus bisect each other.All sides of a rhombus are congruent.∴OS=OQIn △ROQ,OQ=√202−142 ...... By Pythagoras theoremOQ=√400−146OQ=√204SQ=2√204 cm .... (S-O-Q)

The correct option is B $2 \sqrt{204}$ cm
Diagonals of rhombus bisect each other.
All sides of a rhombus are congruent.

$∴ O S = O Q$

In $△ R O Q, O Q = \sqrt{20^{2} - 14^{2}}$ ...... By Pythagoras theorem

$O Q = \sqrt{400 - 146}$

$O Q = \sqrt{204}$

$S Q = 2 \sqrt{204}$ cm .... (S-O-Q)