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