Answer:
L = 12ft
W = 13ft
Explanation:
Let's use the two pieces of information to make 2 equations (we need 2 eqns to solve for 2 variables: Length and Width).
The length and width are consecutive integers
L+1=W
The area of the rectangle is 156 square feet.
L*W=156
We know that W=L+1 from our first equation, so substituting that information into our second equation we get
L*(L+1)=156
Let's distribute that L
L^2 + L = 156
and subtract 156 from both sides
L^2 + L - 156 = 0
Now we can use the quadratic formula to find L. L cannot be negative, so
L = 12
using our very first equation we know L, so we can solve for W.
L+1=W
12+1=W
W = 13