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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out

(A) 4 feet
(B) 5 feet
(C) 6 feet
(D) 7 feet
(E) 8 feet

答案和解析

答案：E

解析：

The ladder, the wall, and the ground form a right triangle with a 25-foot hypotenuse. At first, the bottom of the ladder is 7 feet from the base of the building, so one leg of the right triangle measures 7 feet; the length of the other leg, x, can be found by solving (7^2) + (x^2) = (25^2), which is the Pythagorean theorem. From this, you can figure out that the other leg measures 24 feet.

After the ladder slips down 4 feet, the 24-foot leg of the right triangle becomes 20 feet long. The other leg then has to be 15 feet long. This length is found by solving (20^2) + (y^2) = (25^2), which is again the Pythagorean theorem.

Since the distance between the bottom of the ladder and the base of the building increases from 7 feet to 15 feet, the amount that the bottom of the ladder slides out is 8 feet.