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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Kennedy 2 years 2021-06-22T16:58:06+00:00 1 Answers 0 views 0

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  1. Eden
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    2021-06-22T17:00:00+00:00
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    Answer:

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

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