Question

analyze the diagram below and complete the instructions that follow.
find the value of y.
a. 18
b. 22
c. 24
d. 28
please select the best answer from the choices provided.
○ a
○ b
○ c

Explanation:

Step1: Identify triangle type

This is a right triangle.

Step2: Calculate hypotenuse length

Use Pythagorean theorem:
$$c = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500} = 50$$

Step3: Use area equality to find $y$

Area via legs = Area via hypotenuse & height:
$$\frac{1}{2} \times 30 \times 40 = \frac{1}{2} \times 50 \times y$$
Simplify:
$$600 = 25y$$
Solve for $y$:
$$y = \frac{600}{25} = 24$$

Answer:

C. 24