Question

Please help me find the answer and explain the process to find the answer of the problem appreciate it :)

Answer 1

Answer:

x = 5

Step-by-step explanation:

Pythagorean Theorem $a^{2}  + b^{2} = c^{2}$

side a = x

side b = x + 7

side c = x + 8

therefore:

$x^{2} + (x+7)^{2} = (x+8)^{2}$

This would result in:

$x^{2}  + x^{2}  + 14x + 49 = x^{2}  + 16x + 64$

Let's combine our like terms:

$2x^{2}  + 14x + 49 = x^{2}  +16x + 64$

This looks like a mess, but now we need to take all the value from the right side and move them to the left side using inverse operations. This would result in:

$2x^{2}  - x^{2}  + 14x - 16x + 49 - 64 = 0$

Again, combine like terms:

$x^{2} - 2x - 15 = 0$

Now we factor:

(x-5)(x+3) = 0

Solving gives us:

x - 5 = 0 or x = 5 and x+3 = 0 or x = -3

Since we cannot have a negative distance we can discard the -3.

We plug in the 5 for X making the following:

Side a = 5

Side b = 12

Side c = 13

Check our Work

$5^{2}  + 12^{2}  = 13^{2}$

25 + 144 = 169

169 = 169 is true so x is indeed 5.

Whew!