If Δ ABC ~ ΔQRP, \(\rm \frac{ar(ΔABC)}{ar(ΔQRP)}\) = \(\frac{9}{4}\), AB = 18 cm, BC = 15 cm, then the length of PR is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 4)

Answer 1

Given:

Δ ABC ~ ΔQRP

\(\rm \frac{ar(ΔABC)}{ar(ΔQRP)}\) = \(\frac{9}{4}\)

AB = 18 cm

BC = 15 cm

Concept used:

The ratio of the area of two similar triangles is equal to the square of the ratio of the corresponding side of the triangle

Calculations:

As we know,

The triangle is similar to each other,

Then the corresponding side of BC is PR

So,

⇒ \(\rm \frac{ar(ΔABC)}{ar(ΔQRP)}\) = \(BC^2\over PR^2\)

⇒ \(\frac{9}{4}=\frac{15^2}{PR^2}\)

⇒ \(\frac{3}{2}=\frac{15}{PR}\)

⇒ PR = 10 cm

⇒ Hence, The length of PR is 10 cm

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