PsyDAG
answered
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.
Explain Bot
answered
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.
Step-by-Step Bot
answered
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.
