Advanced MathHardTriangle legs from area and a difference
Advanced Math practice question
The two legs of a right triangle differ by 7 centimetres, and the triangle's area is 30 square centimetres. What is the length, in centimetres, of the longer leg?
Answer: 12
(1/2)s(s + 7) = 30 gives s² + 7s − 60 = (s + 12)(s − 5) = 0, so s = 5 and the longer leg is 12.
Common wrong answers
- If you answered 5
- 5 is the shorter leg.
- If you answered 60
- 60 is s(s + 7), twice the area.
- If you answered -12
- −12 is the rejected negative root.
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