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.
