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Introduction to Similar Triangles

If ΔABC ∼ ΔPQ...

Question

If $Δ A B C \sim Δ P Q C, B C = 16 c m, A B = 10 c m,$ and $P Q = 5 c m$ , then find the measure of $Q R$ .
[1 Mark]

A. $5 c m$
B. $7 c m$
C. $28 c m$
D. $8 c m$

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Solution

Correct option: D
(1 Mark)

Given, $Δ A B C \sim Δ P Q C$

$⟹ \frac{Q R}{B C} = \frac{P Q}{A B}$

$⟹ Q R = \frac{P Q \times B C}{A B} = \frac{5 \times 16}{10} = 8 c m$

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Q. Question 11

I f Δ A B C \sim Δ Q R P,

\frac{a r (Δ A B C)}{a r (Δ P Q R)} = \frac{9}{4}

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\frac{20}{3} c m

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∠ R = ∠ P

and QR =4 cm and PR =5cm. Then, the length of PQ is
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[1]

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5 \sqrt{2}

Δ A B C \sim Δ Q R P, \frac{a r (Δ A B C)}{a r (Δ P Q R)} = \frac{9}{4}

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(A) 10 cm
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\frac{20}{3} c m

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