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Question

The sides of triangle ABC measure 5, 6 and 7 units, while the perimeter of PQR is 360 units .
If ABC is similar to PQR, then find the sides of PQR.

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Solution



We have to find the sides of PQR
It is given that ABC~PQR.
Therefore, by the property of similarity,ABPQ=BCQR=ACPRThis is also equal to AB+BC+ACPQ+QR+PR.ABPQ=BCQR=ACPR= AB+BC+ACPQ+QR+PRABPQ=AB+BC+ACPQ+QR+PR5PQ=5+6+7360PQ=360×518PQ=100 units. BCQR= AB+BC+ACPQ+QR+PR6QR=18360QR=360×618QR=120 units. ACPR= AB+BC+ACPQ+QR+PR7PR=18360

PR = 360×718PR = 140 units

Thus, the sides are 100, 120 and 140 units.

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