Question

The areas of two similar triangles triangle ABC and triangle DEF are 144cm and 81
respectively. If the longest side of larger triangle ABC be 36cm, then, the longest side of
the smaller triangle ADEF is

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Answer 1

Answer:

$\frac{ar(abc)}{ar(def)} = \frac{ {36}^{2} }{ {?}^{2} }$

$\frac{144}{81} = \frac{ {36}^{2} }{ {?}^{2} }$

$144 \times {?}^{2} = {36}^{2} \times 81 \\ {?}^{2} = \frac{36 \times 36 \times 81}{144} \\ {?}^{2} = 729 \\ {?} = \sqrt{729} \\ {?} = 27cm$