Question

Arrange the sides in decreasing order, if ABC and PQR are similar triangles with AB = 20, PQ = 4 and BC =10. Highest value at the top

• A. PQ
• B. AC
• C. QR
• D. PR

Answer 1

Since the given triangles are similar, the ratio of corresponding sides can be written as :

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

$\Rightarrow \frac{20}{4}=\frac{10}{QR}$

$\Rightarrow 5=\frac{10}{QR}$

$\Rightarrow QR=\frac{10}{5}$

$\Rightarrow QR=2$

And, $\frac{20}{4}=\frac{PR}{QR}$

$\Rightarrow$ $5=\frac{PR}{QR}$

$\Rightarrow$ $5=\frac{PR}{2}$

$\Rightarrow$ $PR=10$

Also, $5=\frac{AC}{PR}$

$\Rightarrow$ $5=\frac{AC}{10}$

$\Rightarrow$ $AC=50$

50 > 10 > 4 > 2
AC > PR > PQ > QR