If in a rectangle,the length is increased and | vedclass

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(D) Let the length of the rectangle be $x$ and the breadth be $y$. The area is $A = xy$.According to the first condition: $(x + 2)(y - 2) = xy - 28$.E

Vedclass · Accepted Answer

$253$

Vedclass · Answer

(D) Let the length of the rectangle be $x$ and the breadth be $y$. The area is $A = xy$.According to the first condition: $(x + 2)(y - 2) = xy - 28$.Expanding this: $xy - 2x + 2y - 4 = xy - 28$.Simplifying: $-2x + 2y = -24$,which gives $x - y = 12$ (Equation $1$).According to the second condition: $(x - 1)(y + 2) = xy + 33$.Expanding this: $xy + 2x - y - 2 = xy + 33$.Simplifying: $2x - y = 35$ (Equation $2$).Subtracting Equation $1$ from Equation $2$: $(2x - y) - (x - y) = 35 - 12$,so $x = 23$.Substituting $x = 23$ into Equation $1$: $23 - y = 12$,so $y = 11$.The area of the rectangle is $A = x 	imes y = 23 	imes 11 = 253$ square units.

Part $I$	Part $II$
$1. x+2y=3, 2x+4y=5$	$a. \text{Solution set is a singleton set.}$
$2. 2x+3y=6, x+\frac{3}{2}y=3$	$b. \text{Solution set is an empty set.}$
$3. 3x-y=0, x-y+6=0$	$c. \text{Solution set is an infinite set.}$
	$d. \text{Solution set contains two members.}$

If in a rectangle,the length is increased and breadth reduced each by $2$ units,the area is reduced by $28$ square units. If,however,the length is reduced by $1$ unit and the breadth increased by $2$ units,the area increases by $33$ square units. Find the area of the rectangle.

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