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 :

b or 2, just plug these equations into your graphing calculator then check the graph to see the image. if it matches up then that's your answer!

1. minimum

2. 6400

3. eight

hope this !