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A-2-3-rectangle-and-a-3-4-rectangle-are-contain-within-a-square-without-over-laping-at-any-inferior-point-and-the-sides-of-the-square-are-parallel-to-the-sides-of-the-two-given-rectangles-




Question Number 7519 by Tawakalitu. last updated on 01/Sep/16
A (2 × 3) rectangle and a (3 × 4) rectangle are contain within   a square without over laping at any inferior 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.
$${A}\:\left(\mathrm{2}\:×\:\mathrm{3}\right)\:{rectangle}\:{and}\:{a}\:\left(\mathrm{3}\:×\:\mathrm{4}\right)\:{rectangle}\:{are}\:{contain}\:{within}\: \\ $$$${a}\:{square}\:{without}\:{over}\:{laping}\:{at}\:{any}\:{inferior}\:{point}\:,\:{and}\:{the}\: \\ $$$${sides}\:{of}\:{the}\:{square}\:{are}\:{parallel}\:{to}\:{the}\:{sides}\:{of}\:{the}\:{two}\:{given} \\ $$$${rectangles}.\:{what}\:{is}\:{the}\:{smallest}\:{possible}\:{area}\:{of}\:{the}\:{square}. \\ $$
Commented by Rasheed Soomro last updated on 02/Sep/16
25
$$\mathrm{25} \\ $$
Commented by Yozzia last updated on 02/Sep/16
I think 5^2  also.
$${I}\:{think}\:\mathrm{5}^{\mathrm{2}} \:{also}. \\ $$
Commented by Rasheed Soomro last updated on 02/Sep/16
Sum of smaller sides of the rectangles  should be measure of the side of  required square  (in case maximum of bigger sides is less or equal  to the mentioned sum)  So in this case 2+3=5 is the measure of the side  of the square.  Hence area of the square is of course 5^2 =25.
$${Sum}\:{of}\:{smaller}\:{sides}\:{of}\:{the}\:{rectangles} \\ $$$${should}\:{be}\:{measure}\:{of}\:{the}\:{side}\:{of}\:\:{required}\:{square} \\ $$$$\left({in}\:{case}\:{maximum}\:{of}\:{bigger}\:{sides}\:{is}\:{less}\:{or}\:{equal}\right. \\ $$$$\left.{to}\:{the}\:{mentioned}\:{sum}\right) \\ $$$${So}\:{in}\:{this}\:{case}\:\mathrm{2}+\mathrm{3}=\mathrm{5}\:{is}\:{the}\:{measure}\:{of}\:{the}\:{side} \\ $$$${of}\:{the}\:{square}. \\ $$$${Hence}\:{area}\:{of}\:{the}\:{square}\:{is}\:{of}\:{course}\:\mathrm{5}^{\mathrm{2}} =\mathrm{25}. \\ $$
Commented by Tawakalitu. last updated on 03/Sep/16
Thanks so much
$${Thanks}\:{so}\:{much} \\ $$

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