Question

If $\Delta MNP\sim \Delta RST$, then the value of x is

• A. 24
• B. 20
• C. 32

Answer 1

The correct option is A 24

$\Delta MNP\sim \Delta RST$ (given)

If two triangles are similar, then the ratio of their corresponding sides will be equal.

$\Rightarrow \frac{MN}{RS}=\frac{NP}{ST}=\frac{MP}{RT}$

$\Rightarrow \frac{30}{x}=\frac{15}{12}=\frac{20}{16}$

$\Rightarrow \frac{30}{x}=\frac{5}{4}$

$\Rightarrow 5x=120$

$\Rightarrow x=24$