Answer:
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
