Suppose a rectangular patio has an area of 24 ft² and its length is 2 more than its width. What is its length, width, and perimeter?

Answer 1

Define the variables:

Let x = the width

x+2 = the length

Area = length x width Substitute the numbers into the equation.

24 = x(x+2)

24 = x²+2x Will need to solve this

0 = x²+2x-24 Factor

0 = (x+6)(x-4) Set the factors equal to zero and solve

x+6=0

x=-6 (This is not a valid solution for a width dimension

x-4 = 0

x = 4 ft is the width

This means x+2 = 6 ft for the length

For the perimeter, 4+4+6+6 = 20 ft

Answer 2

Let w = width

A = length x width = (w + 2)w = 24 ft² or w²+2w -24 = 0 this factors to (w+6)(w-4)

w = 4 ft, therefore length = 6 ft and perimeter is equal to 2(4+6) = 20 ft

Please consider a tutor. Take care.

Answer 3

When solving these types of problems, the question is looking to see if you know the formulas for the various measures they're asking for (area, perimeter, etc...). So, for a rectangle:

area = length * width

perimeter = length + length + width + width

For this particular problem we know area = 24, thus the length * width must equal 24. We also know that the length is equal to width + 2. We could go through some more complicated algebraic methods to solve this, but the easiest method is to think about all of the two-number combinations to multiply to get 24.

24 * 1

12 * 2

8 * 3

6 * 4

From these, you need to check for the 2nd condition, that the length is 2 more than the width. Only one of these four combinations matches that requirement.

That gives you the length and width, now all you need to do is solve for the perimeter by adding all four sides together (2 * length plus 2 * width).

Good luck!