Question

The areas of two similar triangles are 25 cm² and 36 cm² respectively. If the altitude of the first triangle is 3.5 cm, then the corresponding altitude of the other triangle is
(a) 5.6 cm
(b) 6.3 cm
(c) 4.2 cm
(d) 7 cm

Answer 1

(c)
We know that the ratio of areas of similar triangles is equal to the ratio of squares of their corresponding altitudes.
Let h be the altitude of the other triangle.
Therefore,

$\frac{25}{36}=\frac{{\left(3.5\right)}^2}{h^2}$
^{$$\begin{gathered} \Rightarrow h^2=\frac{{\left(3.5\right)}^2\times 36}{25} \\ \Rightarrow h^2=17.64 \\ \Rightarrow h=4.2\mathrm{cm} \end{gathered}$$}