Question

Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.

Triangle 1
The distance, along the ground, from the bottom of the ladder to the building is 24 feet. The distance from the bottom of the building to the point where the ladder is touching the building is 32 feet.

Triangle 2
The distance, along the ground, from the bottom of the ladder to the building is 9 feet. The distance from the bottom of the building to the point where the ladder is touching the building is unknown.

Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
8 feet
12 feet
18 feet
27 feet

Answer 1

27

Explanation:

Answer 2

(b) 12 ft

Explanation:

You want the height of a triangle with a base of 9 ft, given that it is similar to a triangle with a base of 24 ft and a height of 32 ft.

Similar triangles

Corresponding sides of similar triangles are proportional. This tells us ...

height/base = height/(9 ft) = (32 ft)/(24 ft)

height = (9 ft)(32/24) = (9 ft)(4/3) = 12 ft

The distance to the top of ladder 2 is 12 feet, choice B.

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