Question

In the given figure below, $\Delta ABC\sim \Delta RPQ$
Choose the correct option(s) (all lengths are in cm).

• A. $RP=1cm$
• B. $\angle Q={73}^{\circ }$
• C. $\angle Q={37}^{\circ }$
• D. $RP=1.5cm$

Answer 1

Answer: (C), (D)

The correct options are
C $\angle Q={37}^{\circ }$
D $RP=1.5cm$

When two triangles are similar, their corresponding angles are equal and corresponding sides are in proportion.

$\Delta ABC\sim \Delta RPQ$ (given)

$\Rightarrow \frac{RP}{AB}=\frac{QP}{CB}and\angle R=\angle A$

$\Rightarrow \frac{RP}{3}=\frac{2}{4}$

$\Rightarrow RP=\frac{3}{2}$

$\Rightarrow RP=1.5cm$

Also,

$\angle R=\angle A={53}^{\circ }$

$\angle R+\angle P+\angle Q={180}^{\circ }$
(using angle sum property)

${53}^{\circ }+{90}^{\circ }+\angle Q={180}^{\circ }$

${143}^{\circ }+\angle Q={180}^{\circ }$

$\angle Q={180}^{\circ }-{143}^{\circ }$

$\angle Q={37}^{\circ }$