Question

The areas of two similar triangles are $16c{m}^2$ and $36c{m}^2$ respectively. If the altitude of the first triangle is $3cm$, then the corresponding altitude of the other triangle is

• A. $6.5cm$
• B. $6cm$
• C. $4cm$
• D. $4.5cm$

Answer 1

The correct option is D $4.5cm$

Given: Area of $two$ similar triangle $16{cm}^2$ and $36{cm}^2$

Altitude of first triangle $=3cm$

For similar triangle,

${\text{Ratio of altitudes}}^2=\text{Ratio of their Area}$

$\therefore$ $\frac{3^2}{x^2}=\frac{16}{36}$

$\frac{9}{x^2}=\frac{16}{36}$

$16x^2=9\times 36$

$x^2=\frac{9\times 36}{16}$

$x^2=\frac{324}{16}=20.25$

$x=4.5cm$