The lengths of the sides of a right angled triangle are ( x+1)cm,4x cm, and (4x+1) cm . Find the value of x

The lengths of the sides of a right angled triangle are x + 1, 4x, and (4x + 1).

Supposing: x + 1 < 4x < 4x + 1

=> Applying Pythagorean theorem:

(x + 1)^2 + (4x)^2 = (4x + 1)^2

=> x^2 + 2x + 1 + 16x^2 = 16x^2 + 8x + 1

=> x^2 - 6x = 0

=>x(x - 6) = 0

=> x = 0 (invalid)

=> x = 6

Check:

=> a = x + 1 = 7,

=> b = 4x = 4*6 = 24,

=> c = 4x + 1 = 4*6 + 1 =25

7^2 + 24^2 = 625 = 25^2

Hope this helps!

:)

The value of x is 6.

Step-by-step explanation:

You have to use Pythagorean Theorem, a² + b² = c². Make (4x+1)cm as the hypotenuse because any values substitute into x will give the highest length among these 3 expressions of length :

Let a = side = (x+1)cm,

Let b = side = 4x cm,

Let c = hypotenuse = (4x+1)cm,

Then you have to simplify :

Next you have to solve it :

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i'm 75% sure the answer is 1,1 to both lines.

have a great day