The ratio of the length to width of a rectangle is 5:8. If the width of the rectangle is 42 inches, what is the perimeter of the rectangle, to the nearest tenth?
Usually the length is longer than the width, but we'll do it your way.
w/42 = 8/5
w = 67.2
p = 2(42 + 67.2) = 218.4
To find the perimeter of a rectangle, you need to know the length and the width of the rectangle. In this case, you are given the width of the rectangle, which is 42 inches. However, you are not given the length directly. You are given the ratio of the length to the width, which is 5:8.
To find the length, you can set up a proportion using the given ratio. Since the ratio of the length to the width is 5:8, you can write:
Length / Width = 5 / 8
Now you can substitute the given width of 42 inches into the equation:
Length / 42 = 5 / 8
To solve for the length, you can cross-multiply:
8 * Length = 42 * 5
Simplifying:
8 * Length = 210
Divide both sides of the equation by 8:
Length = 210 / 8
Length ≈ 26.25 inches
Now that you have both the length and the width, you can calculate the perimeter of the rectangle. The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
Substituting the values you found:
Perimeter = 2 * (26.25 + 42)
Perimeter = 2 * (68.25)
Perimeter = 136.5 inches
Rounding to the nearest tenth:
Perimeter ≈ 136.5 inches