Question

The area of a rectangle gets reduced by 9 $m^2$ if its length is reduced by 5 m and breadth increased by 3 m. if we increase the length by 3 m and breadth by 2 m, the area is increased by 67$m^2$ . The length of the rectangle is

• A. $9$ m
• B. $15.6$ m
• C. $17$ m
• D. $18.5$ m

Answer 1

Answer: (C)

$17$ m

Let the length of rectangle be = $l$
breadth of rectangle = $b$
Then, $lb-(l-5)(b+3)=9$
$5b-3l=-6$ ----(1)
and, $(l+3)(b+2)-lb=67$
$3b+2l=61$---------- (2)
Multiply (1) by 2 and (2) by 3 and add,
$10b+9b=-12+183$
$19b=171$
$b=9$
and, $2.l=61-(3\ast 9)$
Thus, length of rectangle is 17 cm