Im stuck can you help

Question

The length of a rectangle is 5 centimeters more than its width. If the width is increased by 3 centimeters and the length is increased by 5 centimeters, a new rectangle is formed that has an area of 78 square centimeters more than the area of the original rectangle. Find the dimensions of the original rectangle.

Answer 1

JJ,

 

Let L and W be the length and width of the original rectangle. Let A represent the area of the original rectangle. Then we know that

 

L x W = A 

(this is just the formula for area of a rectangle)

 

We are also given that "the length is 5 cm more than the width". Written as an equation, this is

 

L = 5 + W

and I will (suggestively) rewrite this equation as 

L - W = 5

 

Now we have a new rectangle with width W + 3 and length L + 5. Moreover, it says in the problem that the area of this new rectangle is A + 78. Therefore, we get this equation:

 

(W+3) x (L+5) = A + 78

 

If we use foil to multiply here, we get the equation

 

LW + 3L + 5 W + 15 = A + 78

 

Keeping in mind that LW =A, we can write this equation as 

 

A + 3L + 5W + 15 = A + 78

 

Cancelling the A on both sides and subtracting 15 on both sides gives us this equation

 

3L + 5W = 63

 

Remember from the beginning we also have the equation L - W = 5.

So now we have two equations with the two variables L and W. This means we can use a system of equations to find L and W. I think you can take it from here.