Question

ma.8.u7 test25-26

1. nelson is leaning a 22.5 ft ladder against a wall. the base of the ladder is placed 13.5 ft away from the wall.

x ft
22.5 ft
13.5 ft

how high up the wall does the ladder reach?

choose the correct answer from each drop down menu to complete the sentence.

the ladder will reach __choice 1__ up the wall.
choice 1:
a. 36 feet b. 26.24 feet c. 9 feet d. 18 feet

Explanation:

Step1: Apply Pythagorean theorem

$$x^2 + 13.5^2 = 22.5^2$$

Step2: Calculate squared terms

$$x^2 + 182.25 = 506.25$$

Step3: Isolate $x^2$

$$x^2 = 506.25 - 182.25$$
$$x^2 = 324$$

Step4: Solve for $x$

$$x = \sqrt{324}$$
$$x = 18$$

Answer:

D. 18 feet