Question 53

$$\triangle$$ABC $$\sim$$ $$\triangle$$PRQ and PQ = 4 cm, QR = 7 cm and PR = 8 cm. If ar($$\triangle$$ABC) : ar($$\triangle$$PQR) = 1 : 4, then AC is equal to:

Solution

If the two triangles are similar then,

$$\frac{\left(area\ of\ \triangle\ ABC\right)}{\left(area\ of\ \triangle\ PRQ\right)}=\frac{\left(AC\right)^2}{\left(PQ\right)^2}$$

$$\frac{1}{4}=\frac{\left(AC\right)^2}{16}$$

$$AC=2$$

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