8 For a right triangle suppose that the hypotenuse has lengt

8. For a right triangle, suppose that the hypotenuse has length c feet and the lengths of the sides are a feet and b feet.

(a) What is a formula for the area of this right triangle? What is an isosceles triangle?

(b) State the Pythagorean Theorem for right triangles. ?

Solution

a). Area of right angle triangle =ab/2 sq.feet

Isosceles triangle:- A triangle having two equal sides is called as an isosceles triangle.

b). Pythagoras theorem :In a right angle triangle The sum of square of base and height is equal to the square of hypotenuse.

I.e a^2+b^2=c^2

c). Right triangle is an isosceles triangle if a=b

therefore, area of triangle = (1/2)a^2...................(1)

since , given triangle is a right angle triangle

=> a^2+a^2 =c^2

=> 2a^2= c^2

=> a^2 = (c^2)/2

Substitute this value in equation (1)

Hence , Area of triangle = (1/4)c^2