Page 94 - How To Solve Word Problems In Calculus

Solution
Step1
Let x be the side of the square and y the width of the
rectangle.

x 3y

x x y y

x 3y

4x 8y
24"

Step2
2
A = x + 3y 2

Step3
Since the combined perimeter of the two figures must be
24 inches, we have

4x + 8y = 24

x + 2y = 6

It follows that x = 6 − 2y. We can also solve for y. This leads
6 − x
to y = . In order to avoid
2
fractions, we prefer to solve for
x.
Replacing x in terms of y in step 2 gives

2
A(y) = (6 − 2y) + 3y 2
Recall that 4x + 8y = 24. If all of the wire is used to form the
square, y = 0. If all of the wire is used to form the rectangle,
x = 0so8y = 24 and y = 3. Hence

2
A(y) = (6 − 2y) + 3y 2 0 ≤ y ≤ 3
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