Question

Please tell me the solution

Answer 1

 Here ABC is a right angled triangle,

so you can apply the pythagorean theorem.

i.e.sum of squares of AB and BC =square of AC (hypotenuse)

=>  ( x+8)^2 +(x+1)^2 =(x+15)^2

=>   x^2 + 64 +2.x.8+x^2+1+2.x.1 = x^2+225+2.x.15

=>    2x^2 +65 +18x = x^2+225+30.x

=>     2x^2 -x^2 = 225-65 +30x -18x

=>     x^2  = 160 +12x

=>      x^2 -12x -160 =0

=>     x^2 -20x +8x -160 =0

=>     x(x-20) +8(x-20)=0

=>     (x-20) (x+8) =0

=>     x=20 ; x= -8

since length of side cannot be negative, AC =20cm.