Question

find the length of the hypotenuse of $\triangle qpo$.
a. 5
b. 10
c. 12
d. 13

Explanation:

Step1: Apply Pythagorean theorem

$$(x+5)^2 + 5^2 = (x+6)^2$$

Step2: Expand all squared terms

$$x^2 + 10x + 25 + 25 = x^2 + 12x + 36$$

Step3: Simplify the equation

$$x^2 + 10x + 50 = x^2 + 12x + 36$$
$$10x + 50 = 12x + 36$$

Step4: Solve for $x$

$$50 - 36 = 12x - 10x$$
$$14 = 2x$$
$$x = 7$$

Step5: Calculate hypotenuse length

$$x+6 = 7+6 = 13$$

Answer:

D. 13