Question

Find the length of the side $PR$ and $QR$ if the $△ABC$ is similar to $△PQR$ and $\frac{AB}{PQ}=\frac{AC}{PR}$

• A. $PR=3,QR=1$
• B. $PR=4,QR=2$
• C. $PR=4,QR=1.5$
• D. $PR=6,QR=3$

Answer 1

The correct option is C $PR=4,QR=1.5$

The given triangles are


It is given that the triangles are similar.

Therefore, the corresponding side lengths will be proportional.

$\frac{AB}{PQ}=\frac{AC}{PR}$

From the figure, $AB=6$ units, $AC=8$ units and $PQ=3$ units

$\frac{AB}{PQ}=\frac{AC}{PR}$

$\frac{6}{3}=\frac{8}{PR}$

$\frac{2\times 3}{3}=\frac{8}{PR}$

$2=\frac{8}{PR}$

$PR=\frac{8}{2}$

$PR=4$ units

Similarly, $\frac{AB}{AC}=\frac{BC}{QR}$

From the figure, $BC=3$ units

$\frac{6}{3}=\frac{3}{QR}$

$2=\frac{3}{QR}$

$QR=\frac{3}{2}=1.5$ units

Therefore, $PR=4$ units and $QR=1.5$ units