The area of a rectangle is 84 square meters. The length of the rectangle is 5 meters longer than the width. What is the length, in meters, of the rectangle?
To find the length of the rectangle, we can use the formula for the area of a rectangle which is length times width. In this case, we know that the area is 84 square meters.
Let's assume the width of the rectangle is x meters. According to the given information, the length is 5 meters longer than the width, so the length would be x + 5 meters.
Now, we can set up the equation using the formula for the area of a rectangle:
Length * Width = Area
(x + 5) * x = 84
Expanding the equation, we get:
x^2 + 5x = 84
Rearranging the equation:
x^2 + 5x - 84 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula.
Using factoring, we can find two numbers that multiply to -84 and add up to 5. The numbers are -7 and 12:
(x - 7)(x + 12) = 0
Setting each factor to zero, we get:
x - 7 = 0 or x + 12 = 0
Solving for x:
x = 7 or x = -12
Since the width cannot be negative, we take x = 7 as the width.
Substituting x = 7 into the equation for the length (x + 5), we get:
Length = 7 + 5 = 12 meters
Therefore, the length of the rectangle is 12 meters.
Let's assume the width of the rectangle is x meters.
According to the given information, the length of the rectangle is 5 meters longer than the width, so it can be written as x + 5 meters.
The formula for the area of a rectangle is length multiplied by width. So we can write the equation as:
Area = Length × Width
Substituting the given information, we have:
84 = (x + 5) × x
To solve this equation, we can expand it:
84 = x^2 + 5x
Rearranging the equation to form a quadratic equation:
x^2 + 5x - 84 = 0
Now, we can solve this quadratic equation either by factoring, using the quadratic formula, or by completing the square.
If we factorize it, we get:
(x + 12)(x - 7) = 0
Setting each factor equal to zero, we have:
x + 12 = 0 or x - 7 = 0
x = -12 or x = 7
Since length and width can't be negative, the width of the rectangle is 7 meters.
Finally, the length of the rectangle is 5 meters longer than the width, so the length is:
Length = Width + 5 = 7 + 5 = 12 meters
Therefore, the length of the rectangle is 12 meters.
L = W + 5
L * W = 84
Substitute W+5 for L in the second equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.