Question

The areas of two similar triangles are 100cm^2 and 64cm^2. If the altitude of the smaller triangle is 5.5 cm, then what will be the altitude of the corresponding bigger triangle?

(a) 4.4 cm

(b) 4.5 cm

(c) 2.4 cm

(d) 2.5 cm

This question was addressed to me in homework.

This key question is from Area of Similar Triangle topic in section Triangles of Mathematics – Class 10

Answer 1

The correct answer is (a) 4.4 cm

Easiest explanation: We know that the ratio of areas of similar triangles is equal to the ratio of the squares of their corresponding altitudes.

Here the area of ∆ABC is 100cm^2 and area of ∆PQR is 64cm^2. Also, AD = 5.5 cm

According to the theorem,

\(\frac {area \, of \, triangle \, \triangle ABC}{area \, of \, triangle \, \triangle PQR}=(\frac {AD}{PS})\)^2

\(\frac {100}{64}=(\frac {5.5}{PS})\)^2

\(\sqrt {\frac {100}{64}}=\frac {5.5}{PS}\)

\(\frac {5.5}{PS}=\frac {10}{8}\)

PS = \(\frac {5.5}{10} × 8 = \frac {44}{10}\) = 4.4