A rectangle has an area of 24 square units and a perimeter of 20 units. What are its dimensions?

If the length is 4 then the width is 6. If the length is 6 then the width is 4.

Step-by-step explanation:

A rectangle is a 4 sided figure with 4 perpendicular angles. It also have 2 sets of parallel lines which create equal opposite sides. As a result, a rectangle has only length and width as its dimensions. Let length = l and width = w. Use the formula A = l*w to write an equation relating the area of the rectangle with its length and width. It is l*w = 24.

A rectangle also has a perimeter which is the total distance around the shape. The perimeter is found using the formula P = 2l + 2w. So here 20 = 2l + 2w.

This is now a system of equations (2 or more equations with the same variables) and it can be solved using substitution.

l*w = 24

2l + 2w = 20

Begin by solving for w so l*w = 24 becomes w = 24 / l.

2l + 2 (24 / l) = 20

2l + 48 / l = 20

Multiply the whole equation by l to move the variable from the denominator.

2l² + 48 = 20l

2l² - 20l + 48 = 0

Remove the GCF 2 from the quadratic equation.

2 (l² - 10l + 24) = 0

Factor the quadratic equation to solve for l.

2 (l - 4) (l - 6) = 0

Set each factor equal to 0 and solve.

l - 4 = 0 so l = 4

l - 6 = 0 so l = 6

If the length is 4 then the width is 6. If the length is 6 then the width is 4.