Question

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

Answer 1

x = 5

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!