Question

triangle ABC and triangle PQR are similar and AB:PQ = 4:3. If the area of triangle ABC = 48 cm2 , then the area of triangle
PQR in square cm is A. 18 B. 27 C. 64 D. 36​

Answer 1

$Given \: \triangle ABC \sim \triangle PQR \\and \: AB : PQ = 4 : 3$

$Area \: of \: triangle \: ABC = 48 \: cm^{2}$

$\red{ Area \: of \: triangle \: PQR = ? }$

$\underline{\pink{ Proof: }}$

$\triangle ABC \sim \triangle PQR$

$\frac{AB}{PQ} = \frac{4}{3} \: --(1)$

/* We know that , */

$\blue{\frac{Area\: of \: \triangle ABC}{Area\: of \: \triangle PQR} = \frac{AB^{2}}{PQ^{2}} }$

$\implies \frac{48}{Area\: of \: \triangle PQR} = \Big(\frac{AB}{PQ}\Big)^{2}$

$\implies \frac{48}{Area\: of \: \triangle PQR} = \Big(\frac{4}{3}\Big)^{2}$

$\implies \frac{48}{Area\: of \: \triangle PQR} = \frac{16}{9}$

$\implies Area \:of \: \triangle PQR = 48 \times \frac{9}{16}$

$= 3 \times 9 \\= 27 \: cm^{2}$

Therefore.

$Option \: \green { ( B ) } \: is \: correct$

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Answer 2

Answer:

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