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+2 votes
1.2k views
in Mathematics by (6.3k points)
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

1 Answer

+3 votes
by (13.2k points)
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Best answer

 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 = x2   ----- (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

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