7.1.1 Ratio and Proportion (continued)
Example 2 Using Ratios
The ratio of the lengths of the sides of a quadrilateral is used to solve for the length of the longest side in this example. It is given that the sides are in a ratio of 2:3:4:9 and that the perimeter is 126 ft. To solve for the actual length of the longest side, set x to equal the common factor of the side lengths. The actual side lengths can be expressed as the common factor times the ratio number. Write an equation that sets the sum of the side lengths equal to the perimeter and solve for the common factor x . The solution yields x = 7 feet. This is not the answer to the example, which asked for the actual length of the longest side. The length of the longest side is 9 x = 9(7) = 63 feet. A proportion with an unknown is solved here for the value of the unknown. The given proportion is = w 3 60 40 . To solve for the unknown, w , take the cross product of the proportion and solve for w . The solution yields w = 2, meaning that 3 is to 2 as 60 is to 40. This is one of the most useful mathematical procedures to solve simple math questions in everyday life. A proportion with an unknown is solved for the value of the unknown in this example. The given proportion is + = + x x 3 5 20 3 . To solve for the unknown, x , take the cross product of the proportion and solve for x . There are two possible solutions for the unknown: x = 7 or x = − 13.
Example 3 Solving Proportions
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