Question

the length of a rectangular corral is 10 feet less than the width. if the area is 264 square feet, what is the width?

Answer 1

For this case we have that by definition, the area of a rectangle is given by:

$A = w * l$

Where:

w: It is the width

l: It is the length

According to the problem data we have:

$l = (w-10) \ ft\\A = 264 \ ft ^ 2$

So:

$264 = w (w-10)\\264 = w ^ 2-10w\\w ^ 2-10w-264 = 0$

We solve. We look for two numbers that, when multiplied, result in -264 and when added, result in -10. These are:

-22 and 12

So:

$(w-22) (w + 12) = 0$

Thus, the solutions are:

$w_ {1} = 22\\w_ {2} = - 12$

We choose the positive value. So the width of the corral is $22 \ ft$

ANswer:

$22 \ ft$