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

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Solution

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

$\frac{A B}{P Q} = \frac{B C}{Q R} = \frac{A C}{P R}$

$\Rightarrow \frac{20}{4} = \frac{10}{Q R}$

$\Rightarrow 5 = \frac{10}{Q R}$

$\Rightarrow Q R = \frac{10}{5}$

$\Rightarrow Q R = 2$

And, $\frac{20}{4} = \frac{P R}{Q R}$

$\Rightarrow$ $5 = \frac{P R}{Q R}$

$\Rightarrow$ $5 = \frac{P R}{2}$

$\Rightarrow$ $P R = 10$

Also, $5 = \frac{A C}{P R}$

$\Rightarrow$ $5 = \frac{A C}{10}$

$\Rightarrow$ $A C = 50$

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

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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

Since the given triangles are similar, the ratio of corresponding sides can be written as : ABPQ=BCQR=ACPR ⇒204=10QR ⇒5=10QR ⇒QR=105 ⇒QR=2 And, 204=PRQR ⇒ 5=PRQR ⇒ 5=PR2 ⇒ PR=10 Also, 5=ACPR ⇒ 5=AC10 ⇒ AC=50 50 > 10 > 4 > 2 AC > PR > PQ > QR