Question

In the parallelogram shown below, PR = 16cm, PQ = 10 cm what is the length of the
diagonal SQ?

Answer 1

Answer:

PQ= 10 cm

PR=16cm ,so PO=8 cm

In triangle POQ,

OP²+OQ²=PQ²

OQ= √(PQ²– OP²)

or, OQ=√(10²–8²)

or, OQ= 6

So, OQ = 6 cm

SQ=2×OQ= 12cm.

Answer 2

The length of SQ is 12 cm.

Given:

• A parallelogram PQRS.
• PR= 16 cm and PQ=10 cm
• $\angle POQ=90^{\circ}$

To find:

• Length of diagonal SQ.

Solution:

Property of parallelogram: Diagonals of parallelogram bisects each other.

Step 1:

According to the property of parallelogram PO=OR= 8 cm

Step 2:

∆ POQ is right angle triangle.

Two sides are already known, i.e.

PO= 8 cm

PQ= 10 cm

Apply Pythagoras theorem to find OQ.

According to Pythagoras theorem:

Hypotenuse²= Base²+ Perpendicular²

Here

$PQ²= PO²+OQ²$

or

$100 = 64+OQ²$

or

$OQ² = 100 - 64$

or

$OQ² = 36$

or

$\bf OQ = 6 \: cm$

Step 3:

Apply property stated above.

OQ=OS= 6 cm

and

QS= OQ+OS

$QS= OQ+OS$

or

$\bf QS= 6 + 6 = 12 \: cm$

Thus,

Length of SQ is 12 cm.

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