Question

ABC is a right angled triangle with angle B = 90° , 'm' is the midpoint of AC and Bm=√117 cm , AB+BC=30 , then the area of the triangle ABC is?

Answer 1

Answer:

108 cm²

Step-by-step explanation:

by apollonius theorem,in a ∆ the sum of the square of the sides is twice the sum of the squares of median( on the third side) and half of the third side

so,

AB²+BC²=2BM²+2(1/2*AC)²

AC²=2*117+AC²/2. ..........(AB²+BC²=AC²)

AC²/2=2*117

AC=6√13

(AB+BC)²=(30)². (SQUARING BOTH SIDES)

AB²+BC²+2.AB.BC=900

AC²+2.AB.BC=900

4*117+2.AB.BC=900

234+AB.BC=450. (DIVIDING BOTH SIDES BY 2)

AB.BC=216

THUS,AREA OF ∆ABC=1/2*AB*BC

=1/2*216

=108 cm²

I REALLY ENJOYED SOLVING THIS!!