Question

5. In the right triangle shown below, the length of side AB is x, the length of side BC is x + 2, and the length of the
hypotenuse AC is x + 4. Use this information to find the length of each side. (Use the Pythagorean theorem to get
an equation, and solve for x.)

I need an answer quick!!!
It’s from the problem set to lesson 17 M.1

Answer 1

Answer:

$AB = 6$  $BC = 8$   $AC = 10$

Step-by-step explanation:

The picture of the triangle is missing.

Given

$AC = x + 4$

$BC = x + 2$

$AB = x$

Required

Find x

When Pythagoras theorem is applied, we have:

$(AC)^2 = (BC)^2 + (AB)^2$

This is so, because AC is the hypotenuse

So, we have:

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

Open brackets

$x^2 + 4x + 4x + 16 = x^2+2x + 2x + 4 + x^2$

$x^2 + 8x + 16 = x^2+4x + 4 + x^2$

Collect Like Terms

$x^2 -x^2 - x^2 + 8x -4x + 16 - 4 = 0$

$- x^2 + 4x + 12 = 0$

Expand:

$- x^2 + 6x -2x+ 12 = 0$

Factorize:

$-x(x -6) -2(x- 6) = 0$

$(-x -2)(x- 6) = 0$

Split

$-x - 2 = 0$ or $x - 6 = 0$

$-x = 2$ or $x = 6$

$x =-2$ or $x = 6$

Because $BC = x + 2$ and $AB = x$

$x =-2$ can not be considered.

Hence:

$x = 6$

Substitute 6 for x in

$AC = x + 4$

$BC = x + 2$

$AB = x$

$AC = 6 + 4$

$AC = 10$

$BC = 6 + 2$

$BC = 8$

$AB = 6$