Question

the lengths of sides of triangle are x, x+1, x+2 .find the value of x​.
if the given triangle is right angled triangle

Answer 1

Answer:

The sides of a right triangle are x, x + 1 and x + 2. Using Pythagoras' Theorem, (x + 2)^2 = (x + 1)^2 + x^2

=> x^2 + 4x + 4 = x^2 + 2x + 1 + x^2

=> x^2 - 2x - 3 = 0

=> x^2 - 3x + x - 3 = 0=> (x + 1)(x - 3) = 0

=> x = -1 and x = 3

The length of a side cannot be negative, ignore x = -1.

The length of the sides of the right triangle are 3, 4 and 5

Answer 2

✬ Sides = 3 , 4 and 5 ✬

Step-by-step explanation:

Given:

• Length of sides of triangle are x , x + 1 , x + 2.

To Find:

• What is the value of x ?

Solution: Since, it is right angled triangle. So we by using Pythagoras Theorem

★ H² = B² + P² ★

• Longest side (x + 2) will be Hypotenuse.

$\implies{\rm }$ (x + 2)² = x² + (x + 1)²

$\implies{\rm }$ x² + 2² + 2•x•2 = x² + x² + 1² + 2•x•1

$\implies{\rm }$ x² + 4 + 4x = x² + x² + 1 + 2x

$\implies{\rm }$ x² – x² – x² + 4 – 1 = 2x – 4x

$\implies{\rm }$ – x² + 3 = – 2x

$\implies{\rm }$ 0 = x² – 2x – 3

Solving this equation by middle term splitting method.

➨ x² – 2x – 3

➨ x² – 3x + x – 3

➨ x(x – 3) + 1 (x – 3)

➨ (x + 1) and (x – 3)

➨ x + 1 = 0 or x – 3 = 0

➨ x = – 1 or x = 3

[ We have to take the positive value of x i.e 3 ]

So, Measure of sides are

• x = 3
• x + 1 = 3 + 1 = 4
• x + 2 = 3 + 2 = 5

_____________

★ Verification ★

➭ 5² = 4² + 3²

➭ 25 = 16 + 9

➭ 25 = 25

$\large\bold{\texttt {Verified }}$