Question

The length and breadth of a rectangle are increased by 10% and 15% respectively. again, the new length is decreased by 20%. the net change in the area of the rectangle is:

Answer 1

let's take length and breadth be 100 each
therefore the 10%increase 110 and 15%increase is 115 therefore total area =12650
now decrease 20% therefore length will be 92 so area is 10120
difference is 2530
%decrease is 20%

Answer 2

Answer:

The net increase in area is 1.2%.

Step-by-step explanation:

Let the length and width of the rectangle be l and w respectively.

The area of the rectangle is

$A=l\times w$

The length and breadth of a rectangle are increased by 10% and 15% respectively.

$l=l+\frac{10}{100}l=l+0.1l=1.1l$

$w=w+\frac{15}{100}w=w+0.15w=1.15w$

Again, the new length is decreased by 20%.

$l=1.1l-1.1l\times \frac{20}{100}=0.88l$

Now the new length is 0.88l and the new width is 1.15w.

$A=0.88l\times 1.15w=1.012lw$

The net change in the area is

$\frac{1.012lw-lw}{lw}\times 100=1.2\%$

Therefore the net increase in area is 1.2%.