Question

Given a right triangle with a horizontal leg labeled as length x, a vertical leg labeled as length x + 7, and the hypotenuse labeled as length 13, what is the value of x?

Answer 1

Using the Pythagorean theorem, we find that the value of x in the described right triangle is 5.

Step-by-step explanation:

The value of x in the given right triangle can be found using the Pythagorean theorem, which relates the legs of a right triangle to its hypotenuse. In terms of the triangle's side lengths provided, the theorem is expressed as x² + (x + 7)² = 13². This equation arises from the general Pythagorean theorem a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse.

To solve for x, expand the equation to get x² + x² + 14x + 49 = 169. Combining like terms, we get 2x² + 14x - 120 = 0. Dividing by 2, the equation simplifies to x² + 7x - 60 = 0. Factor this quadratic equation to find the values of x. The factors that work are (x+12) and (x-5). Since a length can't be negative, x must equal 5.