What will be the value of BC if the area of two similar triangles ∆ABC and ∆PQR is 64cm^2 and 81cm^2 respectively and the length of QR is 15cm.(a) \(\frac {40}{9}\)(b) \(\frac {40}{6}\)(c) \(\frac {4}{3}\)(d) \(\frac {40}{3}\)This question was addressed to me during an online interview.This intriguing question originated from Area of Similar Triangle in division Triangles of Mathematics – Class 10

What will be the value of BC if the area of two similar triangles ∆A

1.	What will be the value of BC if the area of two similar triangles ∆ABC and ∆PQR is 64cm^2 and 81cm^2 respectively and the length of QR is 15cm.(a) \(\frac {40}{9}\)(b) \(\frac {40}{6}\)(c) \(\frac {4}{3}\)(d) \(\frac {40}{3}\)This question was addressed to me during an online interview.This intriguing question originated from Area of Similar Triangle in division Triangles of Mathematics – Class 10
Answer» The correct answer is (d) \(\FRAC {40}{3}\) Easy explanation: We know that the ratio of areas of similar triangles is equal to the ratio of the squares of their corresponding sides. Here the area of ∆ABC is 64cm^2 and area of ∆PQR is 81cm^2. Also, QR = 15 cm According to the theorem, \(\frac {area \, of \, triangle \, \triangle ABC}{area \, of \, triangle \, \triangle PQR}=(\frac {BC}{QR})\)^2 \(\frac {64}{81}=(\frac {BC}{15})\)^2 \(\sqrt {\frac {64}{81}}=\frac {BC}{15}\) \(\frac {BC}{15}=\frac {8}{9}\) BC = \(\frac {8}{9}\) × 15 = \(\frac {4}{3}\)

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