Question

The length of a rectangular driveway is five feet more than three times the width. The area is 350ft2. Find the width and length of the driveway.

Answer 1

Answer:

• width -- 10 ft
• length -- 35 ft

Step-by-step explanation:

We can let x represent the width. Then the length will be represented by (3x+5), a value 5 more than 3 times the width.

The area is the product of length and width, so is ...

  A = (3x +5)(x) = 3x^2 +5x

To make the area 350, we can find the value of x from ...

  3x^2 +5x = 350

This can be solved a number of ways. One of them is "completing the square".

  3(x^2 +5/3x) = 350

We choose to divide by 3 and add the square of half the x-coefficient.

  x^2 +5/3x +(5/6)^2 = (350/3) + (5/6)^2

  (x +5/6)^2 = 4225/36 . . . . simplify

  x +5/6 = ±√(4225/36) = ±10 5/6 . . . . take the square root

  x = 10  or  -11 2/3 . . . . subtract 5/6

The positive solution is the one of interest: x = 10.

The driveway is 10 ft wide and 35 ft long.