Street Dimensions (Refer to Example 1.) A street has a constant width w and comprises seve...

Street Dimensions (Refer to Example 1.) A street has a constant width w and comprises several straight sections having lengths 600, 400, 350, and 220 feet.

(a) Write a simplified expression that gives the square footage of the street.

---

(b) Find the area of the street if its width is 42 feet.

EXAMPLE 1 Writing and simplifying an expression

A sidewalk has a constant width w and comprises several short sections with lengths 12, 6, and 5 feet, as illustrated in Figure 1.

Figure 1

(a) Write and simplify an expression that gives the number of square feet of sidewalk.

---

(b) Find the area of the sidewalk if its width is 3 feet.

Solution

(a) The area of each sidewalk section equals its length times its width w. The total area of the sidewalk is

 12w + 6w + 5w = (12 + 6 + 5)w = 23w.

---

(b) When w = 3, the area is 23w = 23 • 3 = 69 square feet.