## Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenus

Question

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to sum of the area of triangles on the other two sides.

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Mathematics
2 years
2021-06-22T16:58:06+00:00
2021-06-22T16:58:06+00:00 1 Answers
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## Answers ( )

Answer:Area(ΔPAB) + Area(ΔQBC) = Area (ΔRAC). Proof. Since, triangles PAB, QBC and RAC are equilateral. Therefore they are equiangular and hence similar.