Question

The area of a rectangular wall of a barn is 144 square foot. Its length is 10 foot longer than the width. Find the length and width of the wall of the barn.
The width is ___ feet?

Answer 1

9514 1404 393

Answer:

• width: 8 ft
• length: 10 ft

Step-by-step explanation:

The area is the product of length and width:

  A = LW

  144 = (w+10)(w)

  w^2 +10w -144 = 0 . . . . . . subtract 144 and put in standard form

  (w +18)(w -8) = 0 . . . . . . . . factor

  w = -18 or 8 . . . . . . . values that make the factors zero, -18 is extraneous

The width of the wall is 8 ft; the length is 18 ft.

_____

Additional comment

The equation is factored by looking for factors of -144 that have a sum of 10. We can choose from the different ways 144 can be factored:

  -144 = -1(144) = -2(72) = -3(48) = -4(36) = -6(24) = -8(18) = -9(16) = -12(12)

The respective sums are 143, 70, 45, 32, 18, 10, 7, 0.

So, the factors of -144 that have a sum of 10 are {-8, 18}. These are the constants that go into the binomial factors.