Question

In the figure below right angled triangle ABC where AB is (x-4)cm, AC=(2x+3)cm and BC=2x+2. Form an equation for x and hence find the length of AB, BC, and AC.​

Answer 1

Answer:

Step-by-step explanation:

You can use Phythagoras theroem applied on right angle trinagles

AC^2 = AB^2 + BC^2

(2x + 3)^2 = (x-4)^2 + (2x +2)^2

Apply identity (a+b)^2 = a^2 +b^2 + 2ab

4x^2 + 9+12x = x^2 +16- 8x +4x^2+4 +8x

Now

Cancel out 8x and 4x^2

You will get

12x +9 = x^2 +16 + 4x

Now you get equation

x^2 - 8x + 7=0

x^2 - 7x - 1x + 7 = 0

Take common

x(x - 7) -1( x -7) =0

(x-7)(x-1) = 0

Hence x= 7 or 1.

Hope it js helpful

Please mark me