Question

The areas of two similar triangles are 12 $c{m}^2$ and 48 $c{m}^2$. If the height of the smaller triangle is 2.1 $cm$, then the corresponding height of the bigger triangle is _____.

• A. 4.41 cm
• B. 8.4 cm
• C. 4.2 cm
• D. 0.525 cm

Answer 1

The correct option is C

4.2 cm

The ratio of the area of two similar triangles is equal to the ratio of the squares of their corresponding heights
So,
$\frac{(Heightofsmaller△{)}^2}{(Heightofbigger△{)}^2}=\frac{12}{48}=\frac{1}{4}$

Let the height of bigger triangle be x

$\therefore$$\frac{(2.1{)}^2}{x^2}=\frac{1}{4}\iff x=\sqrt{4\times (2.1{)}^2}$
$=(2\times 2.1)=4.2cm$