Answer: Let's use the given information to set up two equations, one for the length and one for the area, in terms of the width.
Let x be the width of the rectangle, in meters. Then, according to the problem, the length of the rectangle is 1 meter longer than 3 times the width, or 3x + 1.
The area of a rectangle is given by the formula A = length × width, so we can write:
A = (3x + 1) x
We know that the area is 80 m², so we can substitute this value and solve for x:
80 = (3x + 1) x
Expanding the right side gives:
80 = 3x² + x
Rearranging and setting equal to zero:
3x² + x - 80 = 0
This is a quadratic equation that we can solve using the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
where a = 3, b = 1, and c = -80. Plugging in these values, we get:
x = (-1 ± sqrt(1² - 4(3)(-80))) / 2(3)
x = (-1 ± sqrt(1 + 960)) / 6
x = (-1 ± sqrt(961)) / 6
We can simplify the square root to:
x = (-1 ± 31) / 6
Taking the positive value, we get:
x = 5
So the width of the rectangle is 5 meters. Using the expression we found for the length in terms of the width, the length is:
3x + 1 = 3(5) + 1 = 16
So the dimensions of the rectangle are 5 meters by 16 meters.
Explanation: