The length of a rectangle is 2 meters more than its width. If the area is 63 square meters, what are the length and width?
L=w+2
L x w = 63
(w+2) x w = 63
w^2+2w=63
w^2+2w-63=0
What two factors multiply to -63 and add up to 2? 9 and -7. L=9, W=7
Well, well, well. Looks like we have a little math problem here. Let's call the width of the rectangle "x" meters. According to the information given, the length would then be "x + 2" meters. Now, my dear friend, let's use our multiplying skills and find the area!
Area = Length x Width
63 = (x + 2) x x
Simplifying this equation will give you a quadratic equation. But don't worry, quadratic equations are just rectangles with a bit of a fancy twist! Let's solve it and find the dimensions, shall we?
Let's denote the width of the rectangle as x meters.
According to the problem, the length of the rectangle is 2 meters more than its width.
Therefore, the length would be x + 2 meters.
The formula for the area of a rectangle is length multiplied by width.
We are given that the area is 63 square meters, so we have the equation:
(x + 2) * x = 63
To find the values of x that satisfy this equation, we need to solve it.
Expanding the equation, we get:
x^2 + 2x = 63
Rearranging the equation, we have:
x^2 + 2x - 63 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula.
Let's factor the equation:
(x - 7)(x + 9) = 0
Setting each factor equal to zero, we get:
x - 7 = 0 or x + 9 = 0
Solving these equations, we find:
x = 7 or x = -9
Since length and width cannot be negative, we discard x = -9.
Therefore, the width of the rectangle is 7 meters.
To find the length of the rectangle, we substitute the value of x back into the expression for length:
Length = x + 2 = 7 + 2 = 9 meters
So, the length and width of the rectangle are 9 meters and 7 meters, respectively.
To find the length and width of the rectangle, we can use the given information that the length is 2 meters more than the width.
Let's assume the width of the rectangle is x meters.
Therefore, the length of the rectangle would be (x + 2) meters.
The formula to calculate the area of a rectangle is given by length × width.
We are given that the area is 63 square meters. Substituting the values into the formula, we have:
(x + 2) × x = 63
Expanding the equation, we get:
x^2 + 2x = 63
Rearranging the equation to solve for x, we have:
x^2 + 2x - 63 = 0
Now, we can solve this quadratic equation using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = 2, and c = -63.
Substituting the values into the quadratic formula, we get:
x = (-2 ± sqrt(2^2 - 4 × 1 × -63)) / (2 × 1)
Simplifying further, we have:
x = (-2 ± sqrt(4 + 252)) / 2
x = (-2 ± sqrt(256)) / 2
x = (-2 ± 16) / 2
This gives us two possible values for x:
x = (-2 + 16) / 2 = 14 / 2 = 7
x = (-2 - 16) / 2 = -18 / 2 = -9
Since we are dealing with lengths, the width cannot be negative. Therefore, the width of the rectangle is 7 meters.
Substituting the value of x into the equation for the length, we have:
Length = x + 2 = 7 + 2 = 9 meters
Therefore, the length of the rectangle is 9 meters and the width is 7 meters.