The area of a rectangular wall of a barn is 252 square ft. its length is 10 ft longer than twice its width. find the lenght and width of the barn

L=9 ft

W=28 ft

Step-by-step explanation:

LW=252

L=10+2W

Plug 2nd into 1st

(10+2W)W=252

Distribute

10W+2W^2=252

Divide both sides by 2

5W + W^2=126

Reorder using commutative property

W^2+5W =126

Subtract 126 on both sides

W^2+5W-126=0

What are two numbers multiply to be -126 and add to be 5?

My scratch paper:

-126=-2(63)

-126=-2(7)(9)

-126=-14(9)

So 14(-9) is -126 and 14+(-9)=5 so these are our magic numbers

(W+14)(W-9)=0

W=-14 or W=9

So W=9 is what makes sense here sense length can't be negative

Now let's go back and find L...

L=10+2W=10+2(9)=10+18=28

think about it deeply and passionately about this property

i am sorry