Question

15. The perimeter of a square and rectangle
are each equal to 48 m and difference
between area is 4 m. The breadth of the
rectangle is:
Mar 10 m
(c) 18 m
(b) 12 m
(d) 20 m​

Answer 1

Step-by-step explanation:

$perimeter \: of \: square = 4s = 48m \\ s = \frac{48}{4} \\ ➵12m \\ side \: of \: sqr = 12m \\ now \: area \: of \: square = {s}^{2} \\ ➵ {12}^{2} \\ ➵ \: 144 {m}^{2}$

$now \: area \: of \: rectangle \: = (144 - 4)m \\ ➵ \: 140m \\ l \times b = 140 \\ b = \frac{140}{l} \\ perimeter \: of \: rectangle = 2(l + b) = 48$

$l + b = 24 \\ l = 24 - b \\ now \\ ➵b = \frac{140}{l} \\b = \frac{140}{24 - b} \\ 24b - {b}^{2} = 140 \\ {b}^{2} - 24b + 140 \\ {b}^{2} - 14b - 10b + 140 \\ b(b - 14) - 10(b - 14) \\ (b - 10)(b - 14) \\ b = 10 \: or \: b = 14$

$if \: b = 10 \\ then \: l = 24 - b \\ 24 - 10 \\ ➵14m \\ if \: b = 14 \\ then \\ l = 24 - 14 \\ ➵10m$

Hope it helps you!