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

\sqrt{204}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

204

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 \sqrt{204}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

408

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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)

Suggest Corrections

Similar questions

Q. Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.

Q. The diagonals

P R

and

Q S

of a Rhombus

P Q R S

are

20 c m

and

48 c m

respectively. Find the length of side

P Q

The diagonals of a quadrilateral PQRS, PR and SQ intersect at O. If QO = OS, then find the area of triangle PQR given PR = 10 cm and altitude ST = 5 cm.

Q. PQRS is a parallelogram and diagonals PR and SQ bisect at O. If PO

= 3.5

cm and OQ

= 4.1

cm. What is the length of the diagonals?

Q. ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm; diagonal BD = 16 cm, then find the length of other diagonal AC.

Join BYJU'S Learning Program

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)