SOLUTION: Ryan is working on a science project. He has a roll of paper with an area of 5040 square inches. He has to cut the paper into four equal pieces. He will need exactly 576 inches of
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-> SOLUTION: Ryan is working on a science project. He has a roll of paper with an area of 5040 square inches. He has to cut the paper into four equal pieces. He will need exactly 576 inches of
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Question 1097466: Ryan is working on a science project. He has a roll of paper with an area of 5040 square inches. He has to cut the paper into four equal pieces. He will need exactly 576 inches of crepe paper to make borders around the four equal pieces. Find the dimensions of the four equal pieces
You can put this solution on YOUR website! The area of the whole roll is 5040 square inches; when divided into 4 equal parts, the area of each will be 5040/4 = 1260 square inches.
He has 576 inches of crepe paper to form the borders of the four pieces; the amount he needs for each piece is 576/4 = 144 inches.
Length times width of each piece is equal to the area:
Length plus width of each piece is equal to the semi-perimeter:
So we need to solve the system of equations
If we try using formal algebra to solve this pair of equations, we end up with a quadratic equation which, if we try to solve it by factoring, requires us to find two numbers whose product is 1260 and whose sum is 72. But that is exactly what the given pair of equations requires. So we might as well skip the algebra and use some good old trial and error.
When I first started that trial and error process, the first pair I saw that with a product of 1260 was 60 times 21. Since the sum of those is 81 and I want a sum of 72, I know the two numbers need to be closer together than 60 and 21. So I doubled the 21 and cut the 60 in half, giving me 30 and 42; and that pair gives me the sum of 72 that I need.
So the dimensions of each of the 4 pieces is 42 inches by 30 inches.
