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Example 5 from Algebra and Trigonometry, 2.3 Models and Applications
The perimeter of a tablet of graph paper is 48 in. The length is in. more than the width. Find the area of the graph paper.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
The standard formula for area is however, we will solve the problem using the perimeter formula. The reason we use the perimeter formula is because we know enough information about the perimeter that the formula will allow us to solve for one of the unknowns. As both perimeter and area use length and width as dimensions, they are often used together to solve a problem such as this one.
We know that the length is 6 in. more than the width, so we can write length as Substitute the value of the perimeter and the expression for length into the perimeter formula and find the length.
Now, we find the area given the dimensions of in. and in.
The area is in.2.
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
A game room has a perimeter of 70 ft. The length is five more than twice the width. How many ft2 of new carpeting should be ordered?
How did it go?