Question

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. please explain the formula

Answer 1

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:

$W(W+15)=A$

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

$(W-2)(W+13)=A-106$

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

$(W-2)(W+13)=W(W+15)-106\\W^2+11W-26=W^2+15W-106\\4W=80\\W=20$

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.