The area of a rectangle is 21 square meters. Find the length and width of the rectangle if its length is 4 meters greater than its widith. using
Area of a rectangle = (width)(Length)
I THINK I FIGURED IT OUT IS IT X=7,3
Right.
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To find the length and width of the rectangle, we can use the formula for the area of a rectangle, which is given by:
Area = width * length
Given that the area is 21 square meters, we can set up the equation:
21 = width * length
We are also given that the length is 4 meters greater than the width. Let's express this relationship as an equation:
length = width + 4
Now we can substitute the expression for the length in terms of the width into the area equation:
21 = width * (width + 4)
Expanding the equation:
21 = width^2 + 4 * width
Rearranging the equation:
0 = width^2 + 4 * width - 21
Now we have a quadratic equation in terms of the width. We can solve this equation to find the width of the rectangle.
To solve the quadratic equation, we can factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:
The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac))/(2a)
In our equation, a = 1, b = 4, and c = -21. Substituting these values into the quadratic formula:
width = (-4 ± √(4^2 - 4 * 1 * -21))/(2 * 1)
Simplifying:
width = (-4 ± √(16 + 84))/2
width = (-4 ± √100)/2
width = (-4 ± 10)/2
We have two possible solutions:
Solution 1: width = (-4 + 10)/2 = 6/2 = 3
Solution 2: width = (-4 - 10)/2 = -14/2 = -7
Since we are dealing with measurements, we discard the negative value (-7) as it does not make sense in this context.
So, the width of the rectangle is 3 meters.
To find the length, we can use the expression we derived earlier:
length = width + 4 = 3 + 4 = 7 meters.
Therefore, the width of the rectangle is 3 meters and the length is 7 meters.