Difference between revisions of "1950 AHSME Problems/Problem 32"
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− | ==Problem== | + | == Problem == |
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A <math>25</math> foot ladder is placed against a vertical wall of a building. The foot of the ladder is <math>7</math> feet from the base of the building. If the top of the ladder slips <math>4</math> feet, then the foot of the ladder will slide: | A <math>25</math> foot ladder is placed against a vertical wall of a building. The foot of the ladder is <math>7</math> feet from the base of the building. If the top of the ladder slips <math>4</math> feet, then the foot of the ladder will slide: | ||
− | <math>\textbf{(A)}\ 9\text{ ft} \qquad | + | <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> |
− | \textbf{(B)}\ 15\text{ ft} \qquad | ||
− | \textbf{(C)}\ 5\text{ ft} \qquad | ||
− | \textbf{(D)}\ 8\text{ ft} \qquad | ||
− | \textbf{(E)}\ 4\text{ ft}</math> | ||
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− | 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=\textbf{(D)} 8 \text{ ft}</math>. | + | == Solution == |
+ | 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>. | ||
− | ==See Also== | + | == See Also == |
{{AHSME 50p box|year=1950|num-b=31|num-a=33}} | {{AHSME 50p box|year=1950|num-b=31|num-a=33}} | ||
[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 01:02, 12 October 2020
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
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
.
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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