Question

find the value of x using the figure to the right.
x = \square (simplify your answer.)

Explanation:

Step1: Identify similar triangles

The two smaller right triangles are similar to the large right triangle, so corresponding sides are proportional: $\frac{x}{6} = \frac{6}{5+x}$

Step2: Cross-multiply to solve for x

$x(5+x) = 6 \times 6$
$x^2 + 5x = 36$
$x^2 + 5x - 36 = 0$

Step3: Factor the quadratic equation

$(x+9)(x-4) = 0$

Step4: Select positive solution

Length cannot be negative, so discard $x=-9$.

Answer:

$4$