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Q.

PQRS is a rectangle. If PQ+QR=7 and PR+QS=10, find the area of the rectangle PQRS.


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a

16 sq. units

b

14 sq. units

c

12 sq. units

d

13 sq. units 

answer is C.

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Detailed Solution

seoDiagonals of Rectangle are always equal
Hence, PR=QS
→PR+QS=10
PR=QS=5
PR2=PQ2+QR2 Pythagoras Theorem
52=PQ2+7-PQ2
25=PQ2+49+PQ2-14PQ
2PQ2-14PQ+24=0
PQ2-7PQ+12=0
PQ2-4PQ-3PQ+12=0
PQPQ-4-3PQ-4=0
PQ-4PQ-3=0
PQ=4 or PQ=3
→QR=3 or QR=4
→Area of rectangle PQRS=4×3 or 3×4
=12 or 12
=12 sq. units
 
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PQRS is a rectangle. If PQ+QR=7 and PR+QS=10, find the area of the rectangle PQRS.