Question

7-4: practice & problem - solving geometry_7 find the value of x using the figure to the right. x = \\(\square\\) (simplify your answer.)

Explanation:

Step1: Identify similar triangles

The large right triangle and the smaller right triangle (with side $x$) are similar, so corresponding sides are proportional.

Step2: Set up proportion

$\frac{x}{10} = \frac{10}{48}$

Step3: Solve for x

Multiply both sides by 10: $x = \frac{10 \times 10}{48} = \frac{100}{48}$

Step4: Simplify the fraction

Reduce $\frac{100}{48}$ to lowest terms: $x = \frac{25}{12}$

Answer:

$\frac{25}{12}$