Answer:
6
Step-by-step explanation:
Use the given information combine with the Pythagorean theorem to set up an equation. The Pythagorean theorem states that ([tex]a^2 + b^2 = c^2[/tex]), where (a) and (b) are the legs of the right triangle (sides that are adjacent to the right angle); and (c) is the hypotenuse (the side opposite to the right angle). Substitute in the given values in the problem,
[tex]a^2 + b^2 = c^2[/tex]
Substitute,
[tex]QO^2 + QP^2 = PO^2[/tex]
[tex]x^2 + 8^2 = (4+x)^2[/tex]
Simplify, distribute
[tex]x^2 + 64 = x^2 + 8x + 16[/tex]
Inverse operations,
[tex]x^2 + 64 = x^2 + 8x + 16\\-x^2\\\\64 = 8x + 16\\-16\\\\48 = 8x\\/8\\\\6 = x[/tex]
