The width of a patio is 5ft less than the length.write an algebraic expression for the area of the patio.Indicate what the variable in the expression represents in your work?

Answer 1

If the width is five feet less than the length, we can say:

W = L - 5

Where "W" is the patio's width, and "L" is the patio's length. Assuming that the patio is rectangular, then we know that it's area will be equal to it's length multiplied by it's width. In that case, we can say:

a = L × W

We can then take those two equations, and combine them into a single one using substitution. We already know that the width "W" is equal to "L - 5". Let's take that value then, and plug it into the second equation:

a = L × (L - 5)

That equation can then be simplified:

a = L2 - 5L

Which gives us the area of the patio with respect to it's length.

You could also do the substitution the other way around, substituting the length with the width. First, we can rewrite our first equation, expressing it like so:

L = W + 5

Now simply plug that one into our second equation:

a = L × W

∴ a = (W + 5) × W

∴ a = W2 + 5W

Giving us the area of the patio with respect to it's width.