Question

Areas of two similar triangles are 49 $c{m}^2$ and 100 $c{m}^2$. If the length of a side of the smaller triangle is 14 cm, the length of the corresponding side of the other triangle is:

• A. 17 cm
• B. 19 cm
• C. 18 cm
• D. 20 cm

Answer 1

The correct option is D 20 cm

Let x be the side length of a side of the bigger triangle corresponding to the side which is of length 14 cm in the smaller triangle.

Areas of similar triangles are proportional to the square on their corresponding sides.

Thus, $\frac{49}{100}=\frac{{14}^2}{x^2}$
$\Rightarrow x=\pm 20$

Since length can’t be negative, the required side length is 20 cm.