Question

In a right angled triangle, equilateral triangles
are drawn on its all sides. Show that the sum
of the areas of triangles on perpendicular sides
is equal to the area of triangle on hypotenuse.​

Answer 1

Answer:

prove : triangle PAB and triangle QBC and triangle RCR similar since all the triangle are equilateral

Two triangle PNB similar triangle QBC similar triangle RCA

Hence,

Area of triangle PAV / area of triangle are RCA.= ab square upon ac square --------------(1)

Area of triangle ABC / area of triangle are = BC square + AC square

------------(2)

Adding equation (1) and (2)

area of triangle PAB / area of triangle RCA + area of triangle QBC / area of triangle RCA = AB square /AC square + BC square / AC square - AB square - BC square / AC Square

area of triangle PAB + area of triangle QBC / area of triangle RCA = AC square / AC square = 1

area of triangle PAB+ area of triangle QBC = area of triangle RCA

Hence proved

I hope it's clear for you