Final answer:
The dimensions of the rectangle are width w = 3 cm and length l = 10cm.
Step-by-step explanation:
Let's denote the width of the rectangle as w and the length as l.
According to the given information:
1. The length is 4 cm greater than twice the width: l = 2w + 4.
2. The area of the rectangle is 30 cm^2: A = lw = 30.
Substitute the expression for l into the area formula:
2w + 4 x w = 30
Combine like terms:
2w^2 + 4w = 30
Rearrange into a quadratic equation:
2w^2 + 4w - 30 = 0
Now, solve for w. You can use the quadratic formula:
w = {-b pm {b^2 - 4ac}^1/2} / {2a}
In this case, a = 2, b = 4, and c = -30.
w = {-4 pm {4^2 - 4(2)(-30)}^1/2} / {2(2)}
w = {-4 pm {256}^1/2} / {4}
w = {-4 pm 16} / {4}
The two possible solutions for w are w = 3 and w = -{4} / {2}. Since the width cannot be negative, we discard the second solution.
Now, use the value of w to find l using the relationship l = 2w + 4:
l = 2(3) + 4 = 6 + 4 = 10
Therefore, the dimensions of the rectangle are: width w = 3 cm and length l = 10 cm.