Question

c) The perimeter of a rectangle is 48m and its area is 135m². Determine the
side of the rectangle.​

Answer 1

$let \: the \: length \: be \: x \\ let \: the \:breadth \: be \: y$

$perimeter \: of \: rectangle = 2(x + y) \\48 =2( x + y) \\ \frac{48}{2} = x + y \\ 24 = x + y \\ x = 24 - y$

$area \: of \: rectangle =x \times y \\ 135 = xy \\ 135 = y(24 - y) \\ 135 = 24y - {y}^{2} \\ 135 - 24y + {y}^{2} = 0 \\ 135 - 15y - 9y + {y}^{2} = 0 \\ 15(9 - y) - y(9 - y) = 0 \\ (9 - y)(15 - y) = 0$

$y = 15 \: or \: y = 9$

$x = 24 - 15 =9 \\ x = 24 - 9 = 15$

A/Q

Length is always greater than breath

So , length = 15 m

breadth = 9 m