Question

Best answer will become brainliest. On a right-angled triangle, one length is x, another is x+1 and the hypotenuse of the triangle is 2x-1. Find x Show your working please, thank you.

Answer 1

x=o mark as braimliest

Answer 2

GIVEN:

• BC = x cm
• AB = x + 1 cm
• AC = 2x - 1 cm

TO FIND:

• What is the value of 'x' ?

SOLUTION:

We have given that, one length is x, another is x+1 and the hypotenuse of the triangle is 2x-1

✎ To find the value of 'x' , we use the Pythagoras theorem:-

$\bf{\star \: (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\: \star}$

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow (AC)^2 = (BC)^2 + (AB)^2}$

$\rm{\dashrightarrow (2x-1)^2 = (x)^2 + (x + 1)^2 }$

Using Identity:-

• (a - b)² = a² - 2ab + b²
• (a + b)² = a² + 2ab + b²

$\rm{\dashrightarrow (4x^2 - 4x + 1) = x^2 + (x^2 + 2x + 1) }$

$\rm{\dashrightarrow 4x^2 - 4x + 1= 2x^2 + 2x + 1}$

$\rm{\dashrightarrow 4x^2 - 4x + 1 -( 2x^2 + 2x + 1 )= 0}$

$\rm{\dashrightarrow 4x^2 - 4x \: \cancel{+ 1} -2x^2 - 2x \: \cancel{- 1} = 0}$

$\rm{\dashrightarrow 2x^2 - 6x = 0}$

$\rm{\dashrightarrow \cancel{2x^2} = \cancel{6x} }$

$\bf{\dashrightarrow x = 3 }$

• BC = x = 3 cm
• AB = x+1 = 3+1 = 4 cm
• AC = 2x-1 = 2(3) -1 = 6-1 = 5 cm

❝ Hence, the sides of a right - angled triangle are 3 cm , 4 cm and 5 cm ❞

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