Question

The area of a rectangular wall of a barn is 39 square feet. its length is 10 feet longer than the width. find the length and width of the wall of the barn.

Answer 1

x(x+10)=39
x²+10x-39=0
(x+13)(x-3)=0
length = 13 ft
width = 3 ft

Answer 2

Let x = the width of the wall
Then x + 10 = the length of the wall

recall: Area of a rectangle is equal to the length times the width.

So: 39 = x(x + 10) or 39 = x^2 + 10x

This is a quadratic equation and can be rewritten as:
$0 = x^{2} + 10x - 39$

You can solve this quadratic by factoring: you get (x + 1 3)(x - 3) = 0 the solutions are x = -13 and x = 3 Only x = 3 makes sense in this problem.

the width of the rectangular wall is 3 and the length is 13