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Simplify Ratios, Solve for Unknowns, and Find Length and Width

This guide explains how to simplify ratios, solve for unknown values in ratios, and find the length and width of rectangles using ratios. Examples and step-by-step solutions are provided.

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Simplify Ratios, Solve for Unknowns, and Find Length and Width

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  1. Example 1 Simplify Ratios Simplify the ratio. 60 cm : 200 cm a. b. SOLUTION a. 60 cm : 200 cm can be written as the fraction . 3 60 ÷ 20 Divide numerator and denominator by their greatest common factor, 20. = 10 200 ÷ 20 60 cm 60 cm 3 ft 200 cm 18 in. 200 cm 3 is read as “3 to 10.” Simplify. = 10

  2. Example 1 Multiply. Divide numerator and denominator by their greatest common factor, 18. Simplify Ratios b. = Substitute 12 in. for 1 ft. = = = 3 ·12 in. 3 ft 36 ÷ 18 2 36 in. 18 in. 18 ÷ 18 1 18 in. 18 in. 2 Simplify. is read as “2 to 1.” 1

  3. Example 2 Use Ratios In the diagram, AB : BC is 4 : 1and AC = 30. Find AB and BC. SOLUTION Let x = BC. Because the ratio of AB to BC is 4 to 1, you know that AB = 4x. AB + BC= AC Segment Addition Postulate 4x + x = 30 Substitute 4xfor AB,x for BC, and 30 for AC. 5x = 30 Add like terms. x = 6 Divide each side by 5.

  4. Example 2 Use Ratios To find AB and BC, substitute 6 for x. AB = 4x = 4 ·6 = 24 BC = x = 6 So, AB = 24 and BC = 6. ANSWER

  5. Example 3 Use Ratios The perimeter of a rectangle is 80 feet. The ratio of the length to the width is 7 : 3. Find the length and the width of the rectangle. SOLUTION The ratio of length to width is 7 to 3. You can let the length l = 7x and the width w = 3x. 2l + 2w= P Formula for the perimeter of a rectangle 2(7x) + 2(3x) = 80 Substitute 7x for l, 3x for w, and 80 for P. 14x + 6x = 80 Multiply. 20x = 80 Add like terms. x = 4 Divide each side by 20.

  6. Example 3 Use Ratios To find the length and width of the rectangle, substitute 4 for x. l = 7x = 7 ·4 = 28 w = 3x = 3 ·4 = 12 The length is 28 feet, and the width is 12 feet. ANSWER

  7. Checkpoint Use Ratios 1. In the diagram, EF : FG is 2 : 1 and EG = 24. Find EF and FG. 2. The perimeter of a rectangle is 84 feet. The ratio of the length to the width is 4 : 3. Find the length and the width of the rectangle. EF = 16;FG = 8 length, 24 ft; width, 18 ft ANSWER ANSWER

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