A rectangle has a length that is 10 less than three times the width. If the rectangle has an area of 8 ft.², what is the width of the triangle?

Question

What is the correct unit to answer with

Answer 1

Area of a rectangle is length times width or

A = L ·W

A = 8

L = -10 + 3W ("10 less than 3 times the width" use this expression in place of the "L")

W = unknown

Put into Area equation: 8 = (-10 + 3W)·W

Distribute

8 = -10W + 3W²

Put everything on the right side of the equation and rearrange it to get

3W² - 10W - 8 = 0

Solve this by factoring (W-4)(3W+2)=0

So W-4 = 0 or W = 4 feet OR 3W + 2 = 0, or 3W = -2, or W = -2/3

Most widths are positive, so the answer should be the Width = 4 feet

Check: L=-10+3(4) = 2

A = L W = 2*4 = 8

Answer is correct!

Answer 2

1. The two sides of the rectangle can be represented by the following expressions: the width w and the length (3w - 10).
2. Multiply the expressions to get a new expression: 3w² - 10w.
3. Factor this new expression to get (3w + 2)(w - 4).
4. Set each factor equal to 0 and solve each equation.
5. 0 = 3w + 2, -2 = 3w, -2/3 = w
6. 0 = w - 4, 4 = w
7. Since you can't have a negative length, substitute w with 4 in each side length.
8. w = 4
9. 3w - 10 = 3(4) - 10 = 12 - 10 = 2
10. 4 x 2 = 8

The width is 4 feet.