Difference between revisions of "1950 AHSME Problems/Problem 32"
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<math>\textbf{(A)}\ 9\text{ ft} \qquad \textbf{(B)}\ 15\text{ ft} \qquad \textbf{(C)}\ 5\text{ ft} \qquad \textbf{(D)}\ 8\text{ ft} \qquad \textbf{(E)}\ 4\text{ ft}</math> | <math>\textbf{(A)}\ 9\text{ ft} \qquad \textbf{(B)}\ 15\text{ ft} \qquad \textbf{(C)}\ 5\text{ ft} \qquad \textbf{(D)}\ 8\text{ ft} \qquad \textbf{(E)}\ 4\text{ ft}</math> | ||
− | == Solution == | + | == Solution 1== |
By the Pythagorean triple <math>(7,24,25)</math>, the point where the ladder meets the wall is <math>24</math> feet above the ground. When the ladder slides, it becomes <math>20</math> feet above the ground. By the <math>(15,20,25)</math> Pythagorean triple, The foot of the ladder is now <math>15</math> feet from the building. Thus, it slides <math>15-7 = \boxed{\textbf{(D)}\ 8\text{ ft}}</math>. | By the Pythagorean triple <math>(7,24,25)</math>, the point where the ladder meets the wall is <math>24</math> feet above the ground. When the ladder slides, it becomes <math>20</math> feet above the ground. By the <math>(15,20,25)</math> Pythagorean triple, The foot of the ladder is now <math>15</math> feet from the building. Thus, it slides <math>15-7 = \boxed{\textbf{(D)}\ 8\text{ ft}}</math>. | ||
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+ | == Solution 2== | ||
== See Also == | == See Also == |
Revision as of 21:00, 24 December 2023
Contents
[hide]Problem
A foot ladder is placed against a vertical wall of a building. The foot of the ladder is feet from the base of the building. If the top of the ladder slips feet, then the foot of the ladder will slide:
Solution 1
By the Pythagorean triple , the point where the ladder meets the wall is feet above the ground. When the ladder slides, it becomes feet above the ground. By the Pythagorean triple, The foot of the ladder is now feet from the building. Thus, it slides .
Solution 2
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 31 |
Followed by Problem 33 | |
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All AHSME Problems and Solutions |
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