Question

A triangle with integral sides is drawn in a circle of radius 5cm so that all the 3 vertices lie on the circle and 2 of them are endpoints of a diameter. Find the area of the triangle in sq.cm.

• A. 24

Answer 1

The correct option is A 24
Given, 2 vertices are endpoints of a diameter. So, length of that side = 2 x radius = 2 x 5 = 10cm.
In a circle, any diameter subtends an angle of 90${}^0$ at any point on the circle.
So, hypotenuse = 10cm
Given the triangle has integral sides.
Let the lengths of those two sides be a, b.
a and b should be integers and $a2+b^2=100$
Only possible solution is 6, 8.
Area of a right angled triangle is half the product of its two shorter sides.
Area $=\frac{1}{2}\times 6\times 8=24sq.cm.$