A rectangle measures 6 inches in length by 9 inches in width. If the rectangle will be enlarged by 250%, what will be the lengths of the sides of the new rectangle?

What percent bigger is the perimeter of the new rectangle, compared to the original?

original area = 54 in^2

new area = 54(2.5) = 135 in^2

Assuming the new rectangle is similar to old one,
length = 9x , width = 6x
54x^2 = 135
x^2 = 2.5
x = √2.5 = 1.58

new length = 9(1.58) = appr. 14.23 in
new width = 6(1.58) = 9.49 in
percentage increase of perimeter = 58%

new perimeter is 158 % of old one

To find the lengths of the sides of the new rectangle, we need to calculate the 250% increase from the original dimensions.

First, let's find the increase by multiplying each side length by 250% (or 2.5):
Length increase: 6 inches x 2.5 = 15 inches
Width increase: 9 inches x 2.5 = 22.5 inches

To find the total length of the new rectangle, add the increase to the original length:
New length: 6 inches + 15 inches = 21 inches

To find the total width of the new rectangle, add the increase to the original width:
New width: 9 inches + 22.5 inches = 31.5 inches

Therefore, the lengths of the new rectangle will be 21 inches by 31.5 inches.

To calculate the percent increase in perimeter, we need to compare the perimeters before and after the enlargement.

The original rectangle's perimeter can be found by adding the lengths of all four sides:
Original perimeter: 2(6 inches) + 2(9 inches) = 12 inches + 18 inches = 30 inches

The new rectangle's perimeter can be found in the same way:
New perimeter: 2(21 inches) + 2(31.5 inches) = 42 inches + 63 inches = 105 inches

To find the percent increase in perimeter, we need to find the difference between the new and original perimeters and express it as a percentage of the original perimeter:

Perimeter increase: New perimeter - Original perimeter = 105 inches - 30 inches = 75 inches

Percent increase: (Perimeter increase / Original perimeter) x 100% = (75 inches / 30 inches) x 100% = 250%

Therefore, the perimeter of the new rectangle is 250% bigger than the original rectangle.