Please Answer this Question. Joanne has a garden that is 9 feet long by 6 feet wide. She wants to increase the dimensions of the garden by the...

In a rectangular figure the area is equal to width multiplied by length of the rectangle. Expressed in the form of an equation

A = w*l

Where A = area ,

w = width = 6 feet, and

l = length = 9 feet

Therefor:

A = 6*9 = 54 feet^2

If both length and width of the rectangle are increased by a common distance x, the area of the enlarged triangle (A') is given by the following equation.

A' = (w + x)*(l + x) = (6 + x)*(9 + x) = 54 + 15x + x^2

If the increase in area of rectangle is 5 times then:

A' = 5*A = 5*54 = 270 feet^2

Therefor 54 + 15x + x^2 = 270

Therefor: x^2 + 15x - 216 = 0

Therefor: x^2 + 24x - 9x - 216 = 0

Therefor: (x + 24)*(x - 9) = 0

Therefor x = 9 or x = - 24.

We reject the negative value of x.  Therefor x = 9.

Thus we will need to add 9 feet to each of width and length of the original rectangle to increase its area 5 times.

Thus the dimensions of expanded rectangle are:

Width = 6 + 9 = 15 feet

Length = 9 +9 = 18 feet

Area = 15*18 = 270 feet^2