Question

If $\Delta ABC\sim \Delta PQR$, $h_1$ and $h_2$ are the heights of $\Delta ABC$ and $\Delta PQR$ respectively AB : PQ = 3 : 5 and $h_2=12cm$, then the value of $h_1$ is

• A. 7.2 cm
• B. 4. 8 cm
• C. 12 cm
• D. 10 cm

Answer 1

The correct option is A 7.2 cm

Given: $\Delta ABC\sim \Delta PQR,AB:PQ=3:5$ and In case of similar triangles, the ratio of their corresponding sides is equal to the ratio of their corresponding heights.
Thus, $\frac{AB}{PQ}=\frac{h_1}{h_2}$ (Given)
As, $\frac{AB}{PQ}=\frac{3}{5}$
$\frac{h_1}{h_2}=\frac{3}{5}$
$\frac{h_1}{12}=\frac{3}{5}$ (Given)
$h_1=\frac{{12}^{\prime }3}{5}$
$h_1=7.2cm$
Hence, the correct answer is option (1)