Advanced MathMediumSide of a square from the area of its extension
Advanced Math practice question
A square garden is extended by 3 metres in one direction and 5 metres in the other, forming a rectangle with an area of 99 square metres. What was the side length, in metres, of the original square?
Answer: 6
(s + 3)(s + 5) = 99 → s² + 8s + 15 = 99 → s² + 8s − 84 = 0 → (s + 14)(s − 6) = 0 → s = 6.
Common wrong answers
- If you answered 9
- 9 is one side of the new rectangle (6 + 3).
- If you answered 11
- 11 is the other side of the new rectangle (6 + 5).
- If you answered -14
- −14 is the other root, impossible for a length.
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