Advanced MathHardTriangle dimensions from area and a relation
Advanced Math practice question
A right triangle's longer leg is 4 units more than its shorter leg, and its area is 48 square units. What is the length of the shorter leg?
Answer: 8
(1/2)s(s + 4) = 48 gives s² + 4s − 96 = (s + 12)(s − 8) = 0, so s = 8.
Common wrong answers
- If you answered 6
- 6 comes from solving s(s + 4) = 48, forgetting to double the area first; s(s + 4) = 96.
- If you answered 12
- 12 is the longer leg (8 + 4), or the size of the rejected root.
- If you answered 96
- 96 is s(s + 4), not s.
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