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 survey plat depicted here shows two lots that form a trapezoid. The measures of the parallel sides are 115.80 ft and 171.00 ft. The height of the trapezoid is 165.97 ft. Find the combined area of the two lots. Round your answer to the nearest hundredth of a square foot.