McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
1. Ratios and Proportions
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Exercise 3 Page 546

With an extended ratio you can express the lengths of the sides with respect to the factor x.

30, 75, 60

Practice makes perfect
An extended ratio compares three or more numbers. In an extended ratio a : b : c, the ratio of the first two numbers is a : b, the ratio of the last two numbers is b : c, and the ratio of the first and last numbers is a : c. We want to find the lengths of the sides of a triangle that fit the given extended ratio. 2 : 5 : 4 This means that we can express the lengths of the sides of the triangle as 2x, 5x, and 4x.
We know that the perimeter of the triangle is 165 units. Therefore, the sum of the side lengths of the triangle is 165. 2x + 5x + 4x=165 Let's solve this equation and find x.
2x+5x+4x=165
â–Ľ
Solve for x
11x=165
x=15
Now, to find the length of each side of the triangle we will substitute x=15 into the expressions for each of the side lengths.
Expression Substitute Simplify
2x 2(15) 30
5x 5(15) 75
4x 4(15) 60

The lengths of the sides are 30 units, 75 units, and 60 units.