Question

Work out the length of x
(The diagram is not drawn accurately)

Answer 1

x = 7

Explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 24² = 25²

x² + 576 = 625 ( subtract 576 from both sides )

x² = 49 ( take square root of both sides )

x =
`√(49)` = 7

Answer 2

Hey ! there

Answer:

• Length of x is 7 cm

Explanation:

In this question we are provided with a right angle triangle having hypotenuse 25 cm , base 24 cm and perpendicular x . And we are asked to find the length of x .

For finding the length of x we'll use Pythagorean Theorem . Pythagorean Theorem states that sum of square of perpendicular and base is equal to the square of hypotenuse in right angle triangle that is ,

`\: \qquad \: \qquad \: \underline{\boxed{ \frak{H {}^(2) = P {}^(2) + B {}^(2) }}}`

Where ,

• H refers to Hypotenuse

• P refers to Perpendicular

• B refers to Base

SOLUTION : -

Here in the triangle ,

• Hypotenuse is 25 cm

• Base is 24 cm

• Perpendicular is x

Applying Pythagorean Theorem :

`\quad \longmapsto \qquad \: (25) {}^(2) = (x ){}^(2) + (24) {}^(2)`

On squaring 24 and 24 we get ,

`\quad \longmapsto \qquad \:625 = (x) {}^(2) + 476`

Subtracting 576 on both sides :

`\quad \longmapsto \qquad \:625 - 576 = (x) {}^(2) + \cancel{ 576} - \cancel{576}`

We get ,

`\quad \longmapsto \qquad \:49 = (x) {}^(2)`

Applying square root on both sides :

`\quad \longmapsto \qquad \: √(49) = \sqrt{(x) {}^(2) }`

We get ,

`\quad \longmapsto \qquad \: \blue{ \underline{\boxed{\frak{7 \: cm = x}}}} \quad \bigstar`

• Henceforth , length of x is ❝ 7 cm ❞ .

Verifying : -

We are verifying our answer by substituting all the values of hypotenuse , perpendicular and base in Pythagorean Theorem . So ,

• ( 25 )² = ( 7 )² + ( 24 )²

• 625 = 49 + 576

• 625 = 625

• L.H.S = R.H.S

• Hence , Verified .

Therefore, our answer is correct .

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