CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
A rectangular plot belonging to Sharma Traders has a perimeter of 70 m and an area of 300 m². What is the length of the longer side?
The longer side is 20 m. Half the perimeter is 35, so the sides satisfy x(35 − x) = 300, which gives x² − 35x + 300 = 0. This factorises as (x − 15)(x − 20) = 0, so the sides are 15 m and 20 m.
- A20 mCorrect
- B15 m
- C25 m
- D30 m
Explanation
Length + breadth = 35, so with length x the breadth is 35 − x. Area: x(35 − x) = 300, so x² − 35x + 300 = 0. Factorise: (x − 15)(x − 20) = 0, so the sides are 15 and 20. The longer side is 20 m. Check: 15 × 20 = 300 and 2(35) = 70. The option 15 m is the shorter side.
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