 # EXAMPLE 2 Use a ratio to find a dimension SOLUTION Painting You are planning to paint a mural on a rectangular wall. You know that the perimeter of the.

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EXAMPLE 2 Use a ratio to find a dimension SOLUTION 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. Write expressions for the length and width. Because the ratio of length to width is 9 : 2, you can represent the length by 9x and the width by 2x. STEP 1

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

EXAMPLE 3 Use extended ratios Combine like terms. SOLUTION Triangle Sum Theorem Divide each side by 6. =30x = 6x6x180 = o x + 2x + 3x ooo ALGEBRA The measures of the angles in CDE are in the extended ratio of 1 : 2 : 3. Find the measures of the angles. Begin by sketching the triangle. Then use the extended ratio of 1 : 2 : 3 to label the measures as x°, 2x°, and 3 x°. The angle measures are 30, 2(30 ) = 60, and 3(30 ) = 90. oo oo o ANSWER

GUIDED PRACTICE for Examples 2 and 3 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. SOLUTION Write expressions for the length and width. Because the ratio of length is 7 : 5, you can represent the length by 7x and the width by 5x. STEP 1

GUIDED PRACTICE for Examples 2 and 3 STEP 2 Solve an equation to find x. Formula for perimeter of rectangle Substitute for l, w, and P. Multiply and combine like terms. =2l + 2wP = 2(7x) + 2(5x) 48 = 24x= 2x Evaluate the expressions for the length and width. Substitute the value of x into each expression. STEP 3 Length = 7x + 7(2) = 14 ft Width = 5x + 5(2) = 10 ft

GUIDED PRACTICE for Examples 2 and 3 Begin by sketching the triangle. Then use the extended ratio of 1 : 3 : 5 to label the measures as x°, 2x°, and 3 x°. Triangle Sum Theorem SOLUTION Combine like terms. Divide each side by 9. =20x = 9x9x180 = x + 3x + 5x 180 oo o o 4. A triangle’s angle measures are in the extended ratio of 1 : 3 : 5. Find the measures of the angles. x 3x 5x The angle measures are 20, 3(20 ) = 60, and 5(20 ) = 100. oo oo o ANSWER

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