Difference between revisions of "1950 AHSME Problems/Problem 32"
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We can observe that the above setup forms a right angled triangles whose base is 7ft and whose hypotenuse is 25ft taking the height to be x ft. | We can observe that the above setup forms a right angled triangles whose base is 7ft and whose hypotenuse is 25ft taking the height to be x ft. | ||
− | <math>x^2 + 7^2 = 25^2</math> | + | <math>x^2 + 7^2 = 25^2</math>\\ |
− | <math>x^2 = 625 - 49</math> | + | <math>x^2 = 625 - 49</math>\\ |
− | <math>x^2 = 576</math> | + | <math>x^2 = 576</math>\\ |
− | <math>x = 24</math> | + | <math>x = 24</math>\\ |
== See Also == | == See Also == |
Revision as of 22:02, 24 December 2023
Contents
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
We can observe that the above setup forms a right angled triangles whose base is 7ft and whose hypotenuse is 25ft taking the height to be x ft.
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See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 31 |
Followed by Problem 33 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
All AHSME Problems and Solutions |
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