Question 60
$$\triangle$$ABC $$\sim$$ $$\triangle$$RQP and AB = 4 cm, BC = 6 cm and AC = 5 cm. If ar($$\triangle$$ABC) : ar($$\triangle$$PQR) = 9 : 4, then PQ is equal to:
Solution
If two triangle are similar then ratio of area of triangle is equals to the ratio of square of corresponding sides.
$$\frac{\left(Area\ of\ \triangle\ ABC\right)}{Area\ of\ \triangle\ PQR}=\frac{AB^2}{PQ^2}$$
$$\frac{9}{4}=\frac{16}{PQ^2}$$ Hence, PQ = $$\dfrac{8}{3}$$ cm .
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