Question

If the perimeter of a square and a rectangle are equal which of the two has greater area .

Answer 1

let the perimeter of square and rectangle be 4a and hence each side of square will be 4a/4=a
it gives,

$area \: of \: square \: = {a \: }^{2}$
and let length and width of rectangle be a-n and a+n respectively where n is less than a and greater than 0
it gives
$area \: of \: rectangle = lb = (a - n)(a + n) \\ area \: of \: rectangle = {a}^{2} - {n}^{2}$
here we are subtracting n square from a square and hence the value of a square will decrease. therefore area of square is greater than area of rectangle .
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