Question

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 1

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 = \(\frac {4}{3}\)