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, BM^{2} + AM^{2}= AB^{2}

117 + y^{2} = x^{2 ----- (1)}

Now in triangle BMC

BM^{2} + MC^{2} = BC^{2}

117 + y^{2} = (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