Use a formula to write an equation, and then solve the problem. (Use 3.14 as an approxima­...

Use a formula to write an equation, and then solve the problem. (Use 3.14 as an approxima­tion for π.) Formulas are found inside the back cover of this book. See Examples.

Example Finding the Dimensions of a Rectangular Yard

Cathleen’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 dimensions of the yard.

FIGURE

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. The length is 5 meters less than twice the width, so the length is L = 2W − 5. See FIGURE 11.

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

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) = 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.

Let s = the length of the shortest side, in feet,

s + 1 = the length of the medium side, in feet, and,

s + 3 = the length of the longest side in feet.

It is a good idea to draw a sketch. See FIGURE 12.

FIGURE

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

Step 4 Solve.

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

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. 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.

FIGURE

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 13.

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

Step 4 Solve.

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

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

is true.

A drum played at the Royal Festival Hall in London had radius 6.5 ft. What was the area of the circular face of the drum? What was the circumference of the drum? (Source: Guinness World Records.)