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A 2 x3 rectangle and a 3 x4 rectangle are contained within a square without overlapping at any interior point, and the sides of the square are parallel to the sides of the two given rectangles. What is the smallest possible area of the square?

anantha narayanan , 7 Years ago
Grade 10
anser 1 Answers
Arun

Last Activity: 7 Years ago

By experimenting, we find that the smallest side length $s$ of a square into which we can fit rectangles with dimensions $a_1\times a_2$ and $b_1\times b_2$ (with $a_1\le a_2$ and $b_1\le b_2$) is $\max(a_2,b_2,a_1+b_1)$, since one of the pairs of dimensions will have to be stacked together. In this case, $s=\max(3,4,2+3)=5$,
so the area of that square will be = 52 = 25 units
Hope it helps

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