Let ∆ABC ~ ∆QPR and ar(∆ABC) over ar (∆PQR)=49 over 144 If…

Let ∆ABC ~ ∆QPR and ${{ar(∆ABC)} \over ar (∆PQR)}={{49} \over 144}$ If AB = 12 cm, BC = 9 cm and AC = 7 cm, then QR (in cm) is equal to :

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 12.

If ∆ABC ~ ∆QPR, then ${{ar(∆ABC)} \over ar (∆PQR)}= (\frac{AB}{QP})^2 = (\frac{BC}{PR})^2 = (\frac{AC}{QR})^2$

Given, AC = 7 cm

Now, $(\frac{7}{QR})^2 = \frac{49}{144}$

⇒ 7/QR = 7/12

⇒ QR = 12 cm

SSC Selection Post 2022 PYQ — Question 56