Question

areas of two similar triangles are 225 sq.cm. 81 sq .cm . if a side of the smaller triangle is 12 cm ,then find the corresponding side of the bigger triangle

Answer 1

assume that triangle ABC similar triangle PQR
bigger triangle ABC and smaller triangle PQR
A(ABC)=225 and A(PQR)=81

we know that
$\frac{abc}{pqr} = \frac{ab {}^{2} }{pq {}^{2} } \\ \frac{225}{81} = \frac{ab {}^{2} }{12 {}^{2} } \\ taking \: square \: root \: on \: both \: side \\ \frac{15}{9} = \frac{ab}{12} \\ ab \times 9 = 15 \times 12 \\ ab = \frac{15 \times 12}{9} \\ \frac{180}{9} \\ ab = 20$