Answer:
length = 35ft, width = 20ft
Step-by-step explanation:
We are working with length (L), width (W), and area (A). We are asked to find the 2 dimensions. The question tells us that L = W + 15, so we can express L in terms of W. However, we still don't know what A is. Since we have 2 unknowns, we somehow need to develop 2 equations to get a solvable system.
We can set up the first equation using the relationship between L and W:
[tex]W(W+15)=A[/tex]
We can set up the second equation using the information in the second sentence:
[tex](W-2)(W+13)=A-106[/tex]
Now we can plug the first equation, already isolated for A, into the second equation and solve for W:
[tex](W-2)(W+13)=W(W+15)-106\\W^2+11W-26=W^2+15W-106\\4W=80\\W=20[/tex]
A pretty nasty-looking equation actually becomes pretty easy to solve. We know the length is 15ft greater than the width, so if W=20, L=35.
