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A right triangle has legs 6 cm and 8 cm and hypotenuse 10 cm. An equilateral triangle is drawn outwards on each of these three sides, so the three equilateral triangles are similar to one another.
Find the ratio of their areas, taken in the order 6 cm side, 8 cm side, 10 cm side.

Class 10Areas of Similar TrianglesGeometry — Similarity
  • A6 : 8 : 10
  • B3 : 4 : 5
  • C27 : 64 : 125
  • D9 : 16 : 25

Step-by-Step Solution

Similar figures standing on the sides have areas in the ratio of the squares of those sides: . Note that , so the equilateral triangle on the hypotenuse equals the other two put together. The options 6 : 8 : 10 and 3 : 4 : 5 leave the lengths unsquared, and 27 : 64 : 125 cubes them instead.
Answer: D) 9 : 16 : 25

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