Triangles $$ABC$$, $$DEF$$ are two similar triangles such that $$\angle B = \angle E = 90^\circ$$, $$AB = 8$$, $$BC = 9$$ and area of the triangle $$DEF$$ is 100 then $$\frac{AC}{DF}$$ is

Solution

Area of $$\triangle ABC = \frac{1}{2} \times 8 \times 9 = 36$$. For similar triangles the ratio of areas is the square of the ratio of corresponding sides, and $$AC$$, $$DF$$ are the corresponding hypotenuses. So $$\frac{AC}{DF} = \sqrt{\frac{36}{100}} = \frac{3}{5}$$.

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