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3. A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of the other leg. Find the lengths of the hypotenuse and the other leg.
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Answer:
Let s = the length of the shorter leg.
The length of the longer leg is 7 + s.
The length of the hypotenuse is 2s - 7.
Use the Pythagorean Theorem.
s2 + (7 + s)2 = (2s - 7)2 ... Now square the binomials to get:
s2 + 49 + 14s + s2 = 4s2 - 28s + 49 ... Combine like terms and reorder them in descending power to get:
2s2 + 14s + 49 = 4s2 - 28s + 49 ... Subtract 2s2 from both sides and subtract 49 from both sides to get:
42s = 2s2 ... Divide both sides by s to get:
42 = 2s ... Divide both sides by 2 to get:
21 = s
The shorter leg is 21 meters long.