Can you help me figure this?

The area of a rectangle is 14 square meters. Find the length and width of the rectangle if it's length is 5 meters greater than its width. Use an equation and the formula for the area of a rectangle=(width)(length). Thank you.

Think about the factors of 14. It should be obvious.

Yes, I can help you solve this problem.

Let's use variables to represent the length and width of the rectangle. Let's say the width is "w" meters. According to the problem, the length is 5 meters greater than the width, so the length would be "w + 5" meters.

The formula for the area of a rectangle is Area = width * length. In this case, the area is given as 14 square meters. So we can set up the equation:

14 = w * (w + 5)

To solve this equation, we need to expand and simplify it:

14 = w^2 + 5w

Now, we have a quadratic equation. To solve it, we can rearrange the equation to bring everything to one side:

w^2 + 5w - 14 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring.

The equation can be factored into:

(w + 7)(w - 2) = 0

Setting each factor equal to zero, we get:

w + 7 = 0 or w - 2 = 0

Solving for w in each equation, we find two possible values for the width: w = -7 or w = 2. Since we cannot have a negative width, we discard the value w = -7.

Therefore, the width of the rectangle is 2 meters.

We can now use this value to find the length, which is 5 meters greater than the width:

Length = 2 + 5 = 7 meters.

So, the length of the rectangle is 7 meters and the width is 2 meters.

By using the equation and the formula for the area of a rectangle, we were able to find the values of the length and width that satisfy the given conditions.