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EXAMPLE 2

Painting. You are planning to paint a mural on a rectangular wall. You know that the perimeter of the wall is 484 feet and that the ratio of its length to its width is 9 : 2 . Find the area of the wall. STEP 1.

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EXAMPLE 2

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  1. Painting You are planning to paint a mural on a rectangular wall. You know that the perimeter of the wall is 484feet and that the ratio of its length to its width is 9 : 2. Find the area of the wall. STEP 1 Write expressions for the length and width. Because the ratio of length to width is 9 : 2, you can represent the length by 9xand the width by 2x. EXAMPLE 2 Use a ratio to find a dimension SOLUTION

  2. STEP 2 Solve an equation to findx. 2l + 2w = P 484 2(9x) + 2(2x) = 484 22x = x 22 = Evaluate the expressions for the length and width. Substitute the value of xinto each expression. STEP 3 The wall is 198feet long and 44feet wide, so its area is 198 ft 44 ft = 8712 ft. 2 EXAMPLE 2 Use a ratio to find a dimension Formula for perimeter of rectangle Substitute for l, w, and P. Multiply and combine like terms. Divide each side by 22. Length= 9x = 9(22) = 198 Width = 2x = 2(22) = 44

  3. ALGEBRA The measures of the angles in CDE are in the extended ratio of 1 : 2 : 3. Find the measures of the angles. o o o o 180 x + 2x + 3x = 6x 180 = x = 30 ANSWER o o o o o The angle measures are 30 , 2(30 ) = 60 , and 3(30 ) = 90. EXAMPLE 3 Use extended ratios SOLUTION Begin by sketching the triangle. Then use the extended ratio of 1 : 2 : 3 to label the measures as x° , 2x° , and 3x° . Triangle Sum Theorem Combine liketerms. Divide each side by 6.

  4. 14 ft, 10 ft 20°, 60°, 100° ANSWER ANSWER for Examples 2 and 3 GUIDED PRACTICE 3. The perimeter of a room is 48 feet and the ratio of its length to its width is 7 : 5. Find the length and width of the room. 4.A triangle’s angle measures are in the extended ratio of 1 : 3 : 5. Find the measures of the angles.

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