Use a formula to solve the problem. (Use 3.14 as an approximation for π.) Formulas are fou...

Use a formula to solve the problem. (Use 3.14 as an approximation for π.) Formulas are found on the inside covers of this book. See Examples.

EXAMPLE Finding the Dimensions of a Rectangular Yard

Cathleen Horne’s backyard is in the shape of a rectangle. The length is 5 m less than twice the width, and the perimeter is 80 m. Find the dimen- sions of the yard.

Step 1 Read the problem. We must find the dimensions of the yard.

Step 2 Assign a variable. Let W = the width of the lot, in meters. Since the length is 5 meters less than twice the width, the length is L = 2W − 5. See FIGURE 9.

FIGURE 9

Step 3 Write an equation. Use the formula for the perimeter of a rectangle.

Step 4 Solve.

Step 5 State the answer. The width is 15 m and the length is 2(15) − 5 = 25 m.

Step 6 Check. If the width is 15 m and the length is 25 m, the perimeter is 2(25) + 2(15) = 50 + 30 = 80 m, as required.

EXAMPLE Finding the Dimensions of a Triangle

The longest side of a triangle is 3 ft longer than the shortest side. The medium side is 1 ft longer than the shortest side. If the perimeter of the triangle is 16 ft, what are the lengths of the three sides?

Step 1 Read the problem. We must find the lengths of the sides of a triangle.

Step 2 Assign a variable.

See FIGURE 10.

FIGURE 10

Step 3 Write an equation. Use the formula for the perimeter of a triangle.

Step 4

Step 5 State the answer. The shortest side, s, has length 4 ft. Then

Step 6 Check. The medium side, 5 ft, is 1 ft longer than the shortest side, and the longest side, 7 ft, is 3 ft longer than the shortest side. Futhermore, the perimeter is 4 + 5 + 7 = 16 ft, as required.

EXAMPLE Finding the Height of a Triangular Sail

The area of a triangular sail of a sailboat is 126 ft2.

(Recall that “ft2” means “square feet.”) The base of the sail is 12 ft. Find the height of the sail.

Step 1 Read the problem. We must find the height of the triangular sail.

Step 2 Assign a variable. Let h = the height of the sail, in feet. See FIGURE 11.

FIGURE 11

Step 3 Write an equation. The formula for the area of a triangle is , where A is the area, b is the base, and h is the height.

Step 4 Solve.

Step 5 State the answer. The height of the sail is 21 ft.

Step 6 Check to see that the values A = 126, b = 12, and h = 21 satisfy the formula for the area of a triangle.

The largest fashion catalogue in the world was published in Hamburg, Germany. Each of the 212 pages in the catalogue measured 1.2 m by 1.5 m. What was the perimeter of a page? What was the area? (Source: Guinness World Records.)