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?
Please help with solving.
1.
width = half the height (x)
w = x/2
2.
area = width * height = x/2 * x
3. x^2/2 = 50 -- multiply by 2:
x^2 = 100 -- take square root:
x = 10
so, the height is 10 and the width is 5.