Question

In AABC, angle B= 90°. Find the sides of the
triangle, if :
(i) AB = (x – 3) cm, BC = (x + 4) cm and
AC = (x + 6) cm
(ii) AB = x cm, BC = (4x + 4) cm and
AC = (4x + 5) cm

Answer 1

Answer:

Step-by-step explanation:

We are given, m∠B=90

o

AB=(x−3) cm

BC=(x+4) cm

AC=(x+6) cm

x=?

From pythagoras theorem,

AC

2

=AB

2

+BC

2

(x+6)

2

=(x−3)

2

+(x+4)

2

∴ x

2

+12x+36=x

2

−6x+9+x

2

+8x+16

∴ x

2

+12x+36=2x

2

+2x+25

∴ 2x

2

−x

2

+2x−12x+25−36=0

∴ x

2

−10x−11=0

∴ x

2

−11x+x−11=0

∴ x(x−11)+1(x−11)=0

∴ (x+1)(x−11)=0

So, x+1=0 or x−11=0

x=−1

​

or

x=11

​