Question

the triangles are similar.
what is the value of x?
5
16
4
\frac{1}{16}

Explanation:

Step1: Identify corresponding sides

Since the triangles are similar, the ratios of corresponding sides are equal. The hypotenuse of the first triangle is 20, and the hypotenuse of the second is 5. The vertical side of the second triangle is 4, and the vertical side of the first is \( x \).

Step2: Set up the proportion

The ratio of hypotenuses is \( \frac{20}{5} \), and the ratio of vertical sides is \( \frac{x}{4} \). Since they are equal:

$$ \frac{20}{5} = \frac{x}{4} $$

Step3: Solve for \( x \)

Simplify \( \frac{20}{5} = 4 \), so:

$$ 4 = \frac{x}{4} $$

Multiply both sides by 4:

$$ x = 4 \times 4 = 16 $$

Answer:

16