Question

Solve for x.

Thank you （っ＾▿＾）

Answer 1

26.833

Explanation:

So I provided a diagram assigned the sides to a variable to make it a bit easier to refer to the sides.

The essence of this problem is going to be Pythagorean Theorem which is a relationship between the sides in a right triangle as follows:
`a^2+b^2=c^2` where c=hypotenuse

So let's solve for "A" using the Pythagorean Theorem to represent it:
`A^2+24^2=x^2`

Btw the reason I used "24" is because I know the length of the entire line is 30, except the side I'm not counting in this is 6 since it's not part of the triangle.

Now let's solve for A^2:
`A^2=x^2-576`

Now represent "B" using the entire triangle:

`x^2+B^2=30^2\\B^2=900-x^2`

We also know that:
`6^2+A^2=B^2` by using the triangle in the top right that's formed using A, B, and 6.

You might now see where this is going. Now let's plug in these representations of A^2 and B^2 into this last equation:

Original Equation:

`6^2+A^2=B^2`

Equations we will use for substitution:

`B^2=900-x^2`

`A^2=x^2-576`

Now let's plug these in for A^2 and B^2

`36+(x^2-576)=`
`900-x^2`

Now let's combine like terms:

`x^2-540=900-x^2`

Now let's move it all to one side

`2x^2-1440=0`

We can use the quadratic formula to solve this and get the following solutions:

`26.833 \text{ and }-26.833`

We can reject the negative solution based on the context thus leaving us with the solution: 26.833