Needed help solving this math problem ?

Question

The length of a rectangle banner is 5 ft. longer than its width. If the area is 84 square ft. what is the dimensions.

The width of the banner would be what?

The length of the banner would be what?

Answer 1

Hey Harry! Another approach is simply to try factors of 84 and see which ones are separated by 5:

4x21 ... nope ... take 3 factor out of the 21 and put it in the 4 ==> 12x7 works :)  Best wishes

Answer 2

With word problems like this, it helps me to imagine what they are talking about. First of all, the problem says the banner is 5 feet longer than it is wide. I imagine a long rectangular sign. Now I try to put this image into math language. First of all, we know that the banner has a specific width, we will call that:

W

It also says that the length of the banner is 5 feet longer than the width, so we can say that the length, L, is equal to the width plus five:

L= W+5

The problem also states that the area is 84 ft². In order to find out what L and W are, we can use the formula for a rectangle:

Area= L x W

84= L x W

To solve this problem, we need to use just one variable. Since we know that the length is the width plus five, we can use substitution to solve for W:

84 = (W+5) x W

84 = W² + 5W

Set the equation to zero to solve for W using the quadratic formula:

0= W² + 5W - 84

W=7, -12

We can throw away the negative answer since a width measurement cannot be negative.

Use the width to find the length:

L= W+5= 7+5=12

Answer 3

Let width W of the rectangle = x

Therefore, by problem statement, length L of the rectangle = x + 5 (5 ft. longer than width)

Area of rectangle = 84 sq ft. (given)

By formula, Area of rectangle = L times W

Therefore

84 = (x + 5) (x)

Or,  84 = x^2 + 5x

subtracting 84 from both sides you get   x^2 + 5x -84 = 0

x^2 + 5x -84 = 0

x^2 + 12x - 7x - 84 = 0  factorization

x(x + 12) - 7(x + 12) taking commons out

x - 7 = 0    OR    x + 12 = 0

x = 7     OR    x = -12

Since the width of the rectangle cannot be negative we can discard the negative value for x, therefore x = 7

x (width of the rectangle) = 7ft

By problem statement, length is x + 5 therefore, length = 12ft

 

Verify: Given area of rectangle is 84sq ft. which is L times W (12 times 7 = 84)