Question

The area of the wall you are going to paint is 50 feet2. If the width is half the height, what are the dimensions of the wall? In answering this problem follow the steps below:

1. Represent the height as ‘x’ and then write the width in terms of x (for example, 2x, 5.5x, 0.5x, 0.3x).
2. Write down the formula for a rectangle’s area.
3. Substitute the values from step 1 and the original problem into the area formula.

What kind of equation do you need to solve in the end of step 3? How would you go about solving that equation? What other kinds of problems would lead you to this type of equation? Finally, what are the answers for the width and height?


Can you please explain step by step how you got the results? So I can best understand how to solve a similar problem? Thanks!

Answer 1

I will follow the suggested steps even though I don't think they are the best approach.
(I will do it the better way after)

let the height be x
then the width = (1/2)x (it said it was half the height)

(1/2)(x)(x) = 50
times 2
x^2 = 100
x=√100 = 10

so the height is 10
and the width is (1/2)(10) = 5

other way: (notice no fractions)
let the width be x
then the height is 2x (notice the width is 1/2 the height)
2x^2 = 50
x^2 = 25
x = √25 = 5

so the width is 5 and the
height is 2x = 10