Question

THE LENGTHS OF SIDES OF TRIANGLE ARE X CM (X + 1) CM AND (X + 2) CM, THE VALUE OF X WHEN TRIANGLE IS RIGHT ANGLED IS.
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Answer 1

Answer:

When it is a right angled triangle,

x² + (x+1)² = (x+2)² (By Pythagoras Theorem. As (x+2) is the largest side, so it may be the hypotenuse)

or, x² + x² + 2x +1 = x² + 4 + 4x

or, 2x² + 2x + 1 = x² + 4x + 4

or, x² - 2x -3 = 0

or, x² - 3x + x - 3 = 0

or, x(x-3) + 1(x-3) = 0

or, (x+1) (x-3) = 0

Therefore, either x+1 = 0 or x-3 = 0

Or, x = -1, 3

As lengths cannot be negative,

Therefore, we omit x = -1

Therefore, x= 3.

The value of x is 3.

Step-by-step explanation:

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Answer 2

Given:

1) The triangle is a right angled triangle.

2) Lengths of the sides are x cm, (x+1) cm and (x+2) cm

To Find:

Value of x=?

Solution:

As we know that,

Hypotenuse is the largest side of a right angled ∆

So, Here (x+2) is the largest side.

According to the Pythagoras theorem,

x²+(x+1) ²=(x+2) ²

x²+x²+2x+1=x²+4x+4

2x²+2x+1=x²+4x+4

2x²-x²+2x-4x+1-4=0

x²-2x-3=0

Here, x²-2x-3 is a quadratic equation.

Let's solve this!

x²-3x+1x-3=0

x(x-3) +1(x-3) =0

(x-3) (x+1) =0

x=3 or x= -1