Question

How to I solve this

Answer 1

The value of x is 7.

We can solve this problem using the Pythagorean Theorem. We know that the length of the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the other two sides. In this case, the hypotenuse is 10 and one of the other sides is x - 6. We can set up the following equation:

`10^2 = (x - 6)^2 + 6^2`

Simplifying both sides, we get:

100 =
`x^2` - 12x + 36 + 36

Subtracting 72 from both sides, we get:

`28 = x^2 - 12x`

Factoring the right side of the equation, we get:

28 = (x - 4)(x - 7)

Setting each factor equal to zero and solving for x, we get:

`x = 4 \text{ or } x = 7`

However, we know that x is greater than 6. Therefore, the only possible solution is x = 7.