SOLUTION: In a triangle ABC DE||BC area of triangle ADE=16cm² DE= 4cm BC=6cm. Find area of triangle ABC

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Question 1034938: In a triangle ABC DE||BC area of triangle ADE=16cm² DE= 4cm BC=6cm. Find area of triangle ABC
Answer by ikleyn(52814) About Me  (Show Source):
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In a triangle ABC DE||BC area of triangle ADE=16cm² DE= 4cm BC=6cm. Find area of triangle ABC
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The triangles ABC and ADE are similar with the corresponding sides ratio of 4%2F6 = 2%2F3.

Then the areas ratio is %282%2F3%29%5E2 = 4%2F9.

Hence, the area of the triangle ABC is 9%2F4 times the area of the triangle ADE, i.e. %289%2F4%29%2A16 = 36 cm%5E2.