if in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by - Maths - Linear Equations in Two Variables

Question

if in a rectangle, the length is increased and breadth reduced
each by 2 units, the area is reduced by 28 sq 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

Gursheen kaur. · Accepted Answer

Let L and B units be the length and breadth of the rectangle.

When the length is increased by 2 units, then the length will be = L+2

and breadth reduced by 2 units, then breadth will be = B-2

∴Acc. to the question,

$\Rightarrow (L + 2) (B - 2) = L B - 28 \Rightarrow L B - 2 L + 2 B - 4 = L B - 28 \Rightarrow - 2 L + 2 B = - 28 + 4 \Rightarrow - 2 (L - B) = - 24 \Rightarrow L - B = 12 - - - - (i)$

Now,

when the length is reduced by 1 unit , then the length will be = L-1

and

the breadth increased by 2 units, the breadth will be = B+2

$\Rightarrow (L - 1) (B + 2) = L B + 33 \Rightarrow L B + 2 L - B - 2 = L B + 33 \Rightarrow 2 L - B = 33 + 2 \Rightarrow 2 L - B = 35 - - - - (i i)$

Now, On subtracting (i) and (ii), we get,

⇒L-B-2L + B = 12-35

⇒-L = -23

⇒L= 23 units.

Put the value of L in equation (i), we get,

⇒L-B=12

⇒23-B=12

⇒B = 11 units.

Area of rectangle = L $\times$ B = 23 $\times$ 11 = 253 sq. units.

30

if in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 sq. 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.