Question

In triangle PQR angle Q is 90 degree and QR is 4cm more than PQ if area of triangle PQR = 96cm^2.... find the sides of the triangle​

Answer 1

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Answer 2

Step-by-step explanation:

</p><p>AreaofΔPQR=

2

1

×QR×PQ

2

1

×(4+PQ)×PQ=96

4PQ+PQ

2

=96×2

4PQ+PQ

2

=192

PQ² + 4PQ - 192 = 0

PQ² + 16PQ - 12PQ - 192

( By Middle Term Split )

PQ(PQ+16) - 12(PQ+16)

(PQ-12)(PQ+16)

PQ - 12 = 0 and PQ + 16 = 0

PQ = 12 cm and PQ = - 16

Length Can't Be Negative

QR = 4 + PQ

QR = 4 + 12

QR = 16 cm

(PR)² = (PQ)² + (QR)²

( By Pythagoras Theorem )

(PR)² = (12)² + (16)²

(PR)² = 144 + 256

(PR)² = 400

PR = √400

PR = 20 cm