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Question
In the given figure, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.
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Solution
Area of ||gm PQRS = PQ x 6
Also,
Area of ||gm PQRS = PS x 8
∴ PQ x 6 = PS x 8
⇒ PQ = `(8"PS")/(6)`
⇒ PQ = `(4"PS")/(3)` ....(i)
Perimeter of ||gm PQRS = PQ + OR + RS + PS
⇒ 42 = 2PQ + 2PS ...(opposite sides of a parallelogram are equal)
⇒ 21 = PQ + PS
⇒ `(4"PS")/(3) + "PS"` = 21 ...[From (i)]
⇒ `(4"PS" + 3"PS")/(3)`
⇒ 7PS = 63
⇒ PS = 9cm
Now,
PQ = `(4"PS")/(3)`
= `(4 xx 9)/(3)`
= 12cm
∴ PQ = 12cm and PS = 9cm.
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