Question

The length of a rectangle is increased by 10%.the breadth if a rectangle is increased by 20%.the perimeter of the rectangle is increased by x%.the range of x is?

Answer 1

Assign values
Let L = 10
Let W = 10 (a square is a rectangle)

Original area = (LW) = 10*10 = 100

L increases by 20 percent:
(1.2)(10) = 12

W decreases by 20 percent:
(0.8)(10) = 8

New area: (12)*(8) = 96

Percent change:\(\frac{New-Old}{Old} * 100\)

\(\frac{96-100}{100}=\)
\((-.04) * 100\) = 4 percent decrease

Algebra
L = length
W = width
Area = (1)LW

Length increases by 20 percent, width decreases by 20 percent:

1.2L * 0.8W = (.96) LW

.96 is 4 percent less than 1

The area decreases by 4 percent.