Question

fill - in - the - blank (1 point)
as shown in the figure, the side lengths of the triangle are 30, 40, and 50, respectively, then the length of? is

Explanation:

Step1: Verify right triangle

Check if $30^2 + 40^2 = 50^2$:
$30^2 + 40^2 = 900 + 1600 = 2500$, $50^2 = 2500$. So it is a right triangle.

Step2: Calculate triangle area

Use legs as base/height:
$\text{Area} = \frac{1}{2} \times 30 \times 40 = 600$

Step3: Use area to find height $?$

Set hypotenuse as base:
$\text{Area} = \frac{1}{2} \times 50 \times ?$
$600 = \frac{1}{2} \times 50 \times ?$

Step4: Solve for unknown length

Rearrange to solve for $?$:
$? = \frac{2 \times 600}{50} = 24$

Answer:

24