7. A rectangle field has an area of 300 square meters and a perimeter of 80 meters. What is the ratio of the length to the width of this field?
The field is 30 by 10. Figure it from there.
To find the ratio of the length to the width of the field, we need to determine the dimensions of the rectangle first. The area and perimeter information can help us solve for the length and width.
Let's assume the length of the rectangle is "l" and the width is "w."
We know that the area of a rectangle is given by the formula: Area = length × width.
In this case, the area is given as 300 square meters, so we have the equation: lw = 300. (Equation 1)
We also know that the perimeter of a rectangle is given by the formula: Perimeter = 2 × (length + width).
In this case, the perimeter is given as 80 meters, so we have the equation: 2(l + w) = 80. (Equation 2)
Now, we can use these two equations to solve for the length and width.
From Equation 2, we simplify: l + w = 40. (Equation 3)
Next, we can use Equation 3 to substitute the value of "l" in Equation 1:
l = 40 - w. (Equation 4)
Substituting Equation 4 into Equation 1:
(40 - w)w = 300.
Expanding the equation:
40w - w^2 = 300.
Rearranging the equation:
w^2 - 40w + 300 = 0.
Now, we can solve this quadratic equation to find the values of "w" (width). Factoring or using the quadratic formula can help with this step.
Once we find the value of "w," we can substitute it back into Equation 4 to find the value of "l" (length).
Finally, with the length and width values, we can calculate the ratio by dividing the length by the width. The ratio of length to width will be the final answer to the question.