Question

PQRS is a rhombus whose diagonals intersect at M. If PQ = 10 cm and diagonal QS = 16 cm. Find the length of diagonal PR.

Answer 1

Step-by-step explanation:

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Answer 2

The length of diagonal PR is 12cm.

Given:

PQ = 10cm

QS = 16 cm

To find:

Length of diagonal PR

Solution:

Diagonals of rhombus bisect each other.

All sides of a rhombus are congruent.

Two diagonals of rhombus meet at 90°

O is the center of both diagonals

OS = OQ

OG = 1/2 * QS = 1/2 * 16 = 8cm

In Δ POQ,

PQ = 10cm

OQ = 8 cm,

Applying Pythagoras,

PQ² = OQ² + OP²

10² = 8² + OP²

OP² = 10² - 8²

OP² = 100 - 64

OP² = 36

OP = √36

OP = 6

PR is a diagonal where O is the center

OP = OR

PR = OP + OR

=  2* OP

= 2*6

= 12cm

The length of diagonal PR is 12cm.

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