# The areas of two similar triangles are 25 cm2 and 36 cm2 respectively.

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

Solution:

(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,

$\frac{25}{36}=\frac{(3.5)^{2}}{h^{2}}$

$\Rightarrow h^{2}=\frac{(3.5)^{2} \times 36}{25}$

$\Rightarrow h^{2}=17.64$

$\Rightarrow h=4.2 \mathrm{~cm}$