ΔАВС ~ ΔРQR, ar(ΔABC) = 16 cm2, ar(ΔPQR) = 144 cm2 and PQ = 6 cm, then the length of BA is ______.

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ΔАВС ~ ΔРQR, ar(ΔABC) = 16 cm2, ar(ΔPQR) = 144 cm2 and PQ = 6 cm, then the length of BA is 2 cm. Explanation: Since △ABC ∼ △PQR, the ratio of their areas is equal to the square of the ratio of corresponding sides: `"ar(ΔABC)"/"ar(ΔPQR)" = ((AB)/(PQ))^2 Given, $\frac{16}{144}$ = ((AB)/6)^2 $\frac{1}{9}$ = ((AB)/6)^2 (AB)/6 = sqrt($\frac{1}{9}$) (AB)/6 = $\frac{1}{3}$ AB = $\frac{6}{2}$` $\therefore$ AB = 2 cm

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