Page 115 - Math Course 3 (Book 2)

Properties of Proportions

Extended Ratios in Triangles
Solve the Item
We can rewrite 5:12:13 as 5x:12x:13x and use In a triangle, the ratio of the measures of three
those measures for the sides of the triangle. sides is 3:4:5, and the perimeter is 42 feet. Find the
Write an equation to represent the perimeter of the measure of the longest side of the triangle.
triangle as the sum of the measures of its sides.

A. 10.5 ft
B. 14 ft
C. 17.5 ft
D. 37 ft
5x 13x

Answer

12x

5x + 12x + 13x = 90 Perimeter. MO. 10 - L1b
30x = 90 Combine like terms.
x = 3 Divide each side by 30. Using Properties of
Use this value of x to find the measures of the Proportions
sides of the triangle.

5x = 5(3) or 15 centimeters. Vocabulary A-Z
12x = 12(3) or 36 centimeters. Let us learn some vocabulary
13x = 13(3) or 39 centimeters.

The shortest side is 15 centimeters. The answer is A.
cross products
Check You can determine whether a proportion is true by
Add the lengths of the sides to make sure that the using cross-products which is accomplished by
perimeter is 90. the cross multiplication. You multiple the extremes
and the means.
15 + 36 + 39 = 90
3 21 = 105
Answer A 5 = 35 = 105 cross product

A portion is true if the two
40 fractions are equivalent
Your Turn! 10 : 20 = 2 : 4 and the cross-products

are equal.
Write a Ratio
40
The country with the longest school year is China
with 251 days. Find the ratio of school days to total
days in a year for China to the nearest tenth. (Use extremes
365 as the number of days in a year.) The “outside” values of a proportion.
A. 0.3
B. 0.5 mean
C. 0.7
D. 0.8 10 : 20 = 2 : 4
extremes means
Extremes
Answer 3 = 21
5 35

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