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Calculate the Area of a Mural Wall Using Ratios and Perimeter

This guide demonstrates how to calculate the area of a rectangular wall designated for a mural painting, given its perimeter and the ratio of its length to width. We start by expressing the length and width in terms of a variable based on the ratio provided, and then set up an equation using the perimeter to find this variable. Finally, we substitute back to determine the final dimensions of the wall and calculate its area. This involves basic algebraic skills to manipulate equations and ratios.

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Calculate the Area of a Mural Wall Using Ratios and Perimeter

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

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

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

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