The area of a rectangular wall of a barn is 72 square feet. Its length is 6 feet longer than the width. Find the length and width of the wall of the barn.

Question

The area of a rectangular wall of a barn is 72 square feet. Its length is 6 feet longer than the width. Find the length and width of the wall of the barn.

Answer 1

Area = length x width

 

Lw = 72

L = w+6

 

w(w+6) = 72

w²+6w=72

w²+6w-72 = 0

 

Factors of -72 that add to 6 are (12)(-6)

 

(w+12)(w-6) = 0

w = -12 or 6

 

Discarding the negative, width is 6 ft

 

Length = width + 6 = 12 ft

 

wall is 12 ft by 6 ft

Answer 2

Shireen,

The key equation is that for area, A = L * w

We will plug in what we know so far.

72 = L * w

We are told that the L is 6 more than the w, so L = w + 6

Plug that in.

72 = (w+6) w

72 = w² + 6w

Now we have a quadratic equation. We can solve this by setting it equal to zero, factoring, and setting each factor equal to zero and solving.

0 = w² +6w -72

 

You should be able to factor and solve.  You will end up with one extraneous root -- a negative value for w which will work in the equation but not in the real world; we don't measure width in negative numbers.  You just throw it away and keep the positive number.  Then solve for L.

You can do it!

Let me know if you run into any problems, though.

Mary