2015年8月2日SAT官方逐日一題
標題範例: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
謎底:E
【剖析】
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 7²+x²=25² , 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 20feet long. The other leg then has to be 15 feet long. This length is found by solving 20²+y²=25², 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.