Question

The length of three sides of a right angled triangle are ( x -2) cm , x cm and ( x + 2) cm. The value of x is:

Answer 1

Given :

• First side = (x + 2) cm

• Second side = x cm

• Third side = (x - 2) cm

To find :

The value of x.

Solution :

Since , it's right-angled Triangle , we get the sides of the triangle as :

• Hypotenuse = (x + 2) cm.

• Base = x cm.

• Height = (x - 2) cm.

Now if we will use the Pythagoras theorem , we will be able to find the required value.

Pythagoras theorem :

$\boxed{\bf{H^{2} = B^{2} + P^{2}}}$

Where :

• H = Hypotenuse
• B = Base
• P = Hypotenuse

Now using the Pythagoras theorem and substituting the values in it, we get :

$:\implies \bf{H^{2} = B^{2} + P^{2}}$

$:\implies \bf{(x + 2)^{2} = x^{2} + (x - 2)^{2}}$

Using the identity :

• (a + b)² = a² + 2ab + b²

• (a + b)² = a² - 2ab + b²

$:\implies \bf{x^{2} + 2 \times 2 \times x + x^{2} = x^{2} + x^{2} + 2 \times 2 \times x + x^{2}}$

$:\implies \bf{x^{2} + 4x + 2^{2} = x^{2} + x^{2} - 4x + 2^{2}}$

$:\implies \bf{x^{2} + 4x + 2^{2} = 2x^{2} - 4x - 2^{2}}$

$:\implies \bf{0 = - (x^{2} + 4x + 2^{2}) + (2x^{2} - 4x - 2^{2})}$

$:\implies \bf{0 = - x^{2} - 4x - 2^{2} + 2x^{2} - 4x - 2^{2}}$

$:\implies \bf{0 = - x^{2} - 4x - 4 + 2x^{2} - 4x + 4}$

$:\implies \bf{0 = - x^{2} - 4x - 4 + 2x^{2} - 4x + 4}$

$:\implies \bf{0 = x^{2} - 8x}$

$:\implies \bf{0 = x^{2} - 8x)}$

$:\implies \bf{0 = x(x - 8)}$

$:\implies \bf{\dfrac{0}{x} = x - 8}$

$:\implies \bf{0 = x - 8}$

$:\implies \bf{8 = x}$

$\boxed{\therefore \bf{x = 8\:cm}}$

Hence, the value of x is 8.

Answer 2

Answer:

Step-by-step explanation: