## Quant Question of The Day: 175

# Algebra

**Rajat has a rectangle of integer side lengths a and b, and area 1000. What is the smallest perimeter it could have?**

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**Rajat has a rectangle of integer side lengths a and b, and area 1000. What is the smallest perimeter it could have?**

To minimize the sum of the side lengths, we need to keep the length and width as close as possible, because the square has the smallest perimeter of all rectangles with a fixed area. So, 40 and 25 multiply to 1000 and are as close as possible – the 40 x 25 rectangle has perimeter 130.

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