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 rectangleSubstitute for l, w, and P.Multiply and combine like terms.Divide each side by 22.

=2l + 2w P=2(9x) + 2(2x) 484= 48422x

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 is198 ft 44 ft = 8712 ft .2

= 22x

Length = 9x = 9(22) = 198Width = 2x = 2(22) = 44

EXAMPLE 3 Use extended ratios

Combine like terms.

SOLUTION

Triangle Sum Theorem

Divide each side by 6.= 30x=6x 180= 180o

x + 2x + 3x o oo

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 3x° .

The angle measures are 30 , 2(30 ) = 60 , and 3(30 ) = 90.o o o o oANSWER

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 rectangleSubstitute for l, w, and P.Multiply and combine like terms.

=2l + 2w P=2(7x) + 2(5x) 48= 4824x= 2x

Evaluate the expressions for the length and width. Substitute the value of x into each expression.

STEP 3

Length = 7x + 7(2) = 14 ftWidth = 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 3x° .

Triangle Sum Theorem

SOLUTION

Combine like terms.Divide each side by 9.= 20x

=9x 180=x + 3x + 5x 180o o oo

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.o o o o oANSWER