Answer:
Width ≈ 6.1 yards
Length ≈ 9.1 yards
Explanation:
Let's use "x" to represent the width of the rectangle.
According to the problem, the length is 3 yards longer than the width, so the length can be represented as "x + 3".
We know that the area of the rectangle is 46 yards squared, so we can set up the equation:
x(x + 3) = 46
Expanding the left side of the equation:
x^2 + 3x = 46
Moving all terms to one side:
x^2 + 3x - 46 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 3, and c = -46. Plugging in these values, we get:
x = (-3 ± sqrt(3^2 - 4(1)(-46))) / 2(1)
x = (-3 ± sqrt(193)) / 2
We can discard the negative root because the width of the rectangle cannot be negative. So:
x = (-3 + sqrt(193)) / 2
x ≈ 6.1
So the width of the rectangle is approximately 6.1 yards.
The length can be found by adding 3 yards to the width:
x + 3 ≈ 9.1
So the length of the rectangle is approximately 9.1 yards.
Rounding to the nearest tenth, we have:
Width ≈ 6.1 yards
Length ≈ 9.1 yards