wall of a barn 7

Question

The area of a rectangular wall of a barn is
216
square feet. Its length is
6
feet longer than twice its width. Find the length and width of the wall of the barn.

Answer 1

The key here is finding expressions for the lengths of the two sides with just one variable.

 

If the width is x (in feet), then the length is twice this plus 6 feet, or 2x + 6.

 

The other thing we know is that its area is 216, so, since length x width = area, x(2x + 6) = 216.

 

Distribute the x: 2x² + 6x = 216. 

 

Now we have a quadratic equation that we can solve with the quadratic formula, or by factoring.

 

The latter is easier, but not always possible. In this case it is.

 

First, I'll divide by 2:  x² + 3x = 108, or x² + 3x - 108 = 0.

 

To factor this, we need two numbers that multiply to -108 and differ by 3. 12 and 9 should do it.

 

So we have (x + 12) (x - 9) = 0.

 

Then x = -12 or 9. -12 doesn't make much sense in the real world, so the width is 9 and the length is 2(9) + 6 = 24.

 

Check: 9 * 24 = 216.