The length of a rectangle is 15 ft greater than its width. if each dimension is decreased by 2 ft, the area will be decreased by 106 ft2. find the dimensions. explain the formula

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:

We can set up the second equation using the information in the second sentence:

Now we can plug the first equation, already isolated for A, into the second equation and solve for W:

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.

-6 is the correct option from the above given options