Question

1.how many non congruent right triangles with positive integer leg lengths have areas that are numerically equal to 3 times their perimeters?

2.a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3.what is the area of the triangle?

3.what is the area of the incircle of a triangle with side lengths 10065,6039 and 8052?

Answer 1

This is a right angled triangle with the sides ratio 3:4:5. It can easily be shown that the radius of the incircle of this triangle is 1, that is one third of the smallest side(3). So that is of the given triangle is 1/3*6039 = 2013. Hence the area of the incircle is phi * 2013^2.