Find the area of the triangle :

Question

ABC is a right angled triangle with angle B=90. M is the midpoint of AC and BM=sq.rt of 117cm. The sum of the sides AB and BC is 30 cm. Find the area of the triangle

Answer 1

 we have AB + BC  = 30

  Let AB = x cm

  BC = 30 – x

In triangle, ABM and BMC

Angle AMB = angle BMC (90º)

 BM = BM (common)

So,  In triangle AMB

Let AM=MC=y

 So, BM² + AM²= AB²

117 + y² = x^{2   ----- (1)}

 Now in triangle BMC

BM² + MC² = BC² 

117 + y² = (30-x)² ------------(2)

From equation 1 and 2 we get,

30-x = x

 x+x = 30

 2x = 30

 x = 30/2

  x = 15

 so, AB = 15

  BC = 30-15 = 15

 Area of triangle = 1/2 *base * height

  =1/2 *AB * BC

  = 1/2*15*15

  = 225/2

  = 112.5 cm²