Chapter: Similarity· Mathematics Part 2 (Geometry)

Asked in: July 2025 board paper\(\Delta ABC\) has sides of length 4 cm, 5 cm and 6 cm while \(\Delta PQR\) has perimeter of 90 cm. If \(\Delta ABC\) is similar to \(\Delta PQR\), then find the length of corresponding sides of \(\Delta PQR\).

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Answer: The sides of \(\Delta PQR\) are 24 cm, 30 cm and 36 cm.

Perimeter of \(\Delta ABC = 4 + 5 + 6 = 15\) cm.

For similar triangles, the ratio of perimeters equals the ratio of corresponding sides: \(\dfrac{\text{perimeter of } \Delta ABC}{\text{perimeter of } \Delta PQR} = \dfrac{15}{90} = \dfrac{1}{6}\).

So each side of \(\Delta PQR\) is 6 times the corresponding side of \(\Delta ABC\).

Sides of \(\Delta PQR\): \(6 \times 4 = 24\) cm, \(6 \times 5 = 30\) cm, \(6 \times 6 = 36\) cm.

Check: \(24 + 30 + 36 = 90\) cm.

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Asked in: July 2025 board paper\(\Delta ABC\) has sides of length 4 cm, 5 cm and 6 cm while \(\Delta PQR\) has perimeter of 90 cm. If \(\Delta ABC\) is similar to \(\Delta PQR\), then find the length of corresponding sides of \(\Delta PQR\).

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