Question

if the sides of a right angled triangle are 2x-1,2x,2x+1.find x value.

Answer 1

By Pythagoras theorem
(2x-1)^2+(2x) ^2 = (2x+1)^2
4x^2+1-4x+4x^2 = 4x^2+1+4x
8x^2-4x^2+1-1 = 8x
4x^2-8x = 0
4x(x-2) = 0
x= 2 or x = 0 ( not possible)
Hence x = 2
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Answer 2

Answer:

The value of x= 2.

Explanation:

Here in this question, we have been given that the three sides of a right-angled triangle are 2x-1, 2x, 2x+1, and we are asked to find the value of x.

Now for doing so, we will apply the Pythagoras theorem as the triangle is a right-angled triangle.

According to the Pythagoras theorem:

AC²= AB² + BC²

⇒(2x+1)² = (2x-1)² +(2x)²

⇒4x²+1+4x = 4x²+1-4x+4x²

⇒4x= 4x²-4x

⇒8x= 4x²

⇒4x²-8x=0

⇒4x(x-2)=0

x=2 or x=0 (not possible)

Hence the required value x is 2.