Question

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

Answer 1

the question is incomplete without figure

Answer 2

• The length of the diagonal SQ of given parallelogram is equal to 12 cm .

Given :- In the parallelogram shown below, PR = 16 cm, PQ = 10cm. ∠POQ = 90° . { Refer to image. }

To Find :- The length of the diagonal SQ ?

Concept used :-

• Diagonals of a parallelogram bisect each other .
• According to pythagoras theorem in a right angled triangle :- (Perpendicular)² + (Base)² = (Hypotenuse)² .

Solution :-

given that,

→ PR = 16 cm

So,

→ PO = OR = 16/2 = 8 cm { since diagonals of a parallelogram bisect each other }

now, in right angled ∆POQ we have,

→ PO = 8 cm { from above }

→ PQ = 10 cm { given }

then,

→ PO² + OQ² = PQ² { By pythagoras theorem }

→ (8)² + OQ² = (10)²

→ 64 + OQ² = 100

→ OQ² = 100 - 64

→ OQ² = 36

→ OQ² = 6²

square root both sides,

→ OQ = 6 cm

therefore,

→ SO = OQ = 6 cm { since diagonals of a parallelogram bisect each other }

hence,

→ SQ = SO + OQ

→ SQ = 6 + 6

→ SQ = 12 cm (Ans.)

The length of the diagonal SQ is equal to 12 cm .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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