the area of a rectangle is 30/sqrt3750 square inches, and the length is 3/sqrt250 inches. what is the width of the rectangle
The area of a rectangle is given by the product of its length and width.
Let's denote the width of the rectangle as w.
So, the area of the rectangle is:
w * (3/sqrt250) = 30/sqrt3750
Multiplying both sides of the equation by sqrt250, we get:
w * 3 = (30/sqrt3750) * sqrt250
w = (30/sqrt3750) * sqrt250 / 3
Now, we can simplify this expression:
w = (30 * sqrt250) / (3 * sqrt3750)
Since sqrt250 = sqrt(25 * 10) = 5 * sqrt10 and sqrt3750 = sqrt(25 * 150) = 5 * sqrt150, we have:
w = (30 * 5 * sqrt10) / (3 * 5 * sqrt150)
The factors of 5 cancel out:
w = (6 * sqrt10) / (sqrt150)
Simplifying sqrt150 = sqrt(25 * 6) = 5 * sqrt6, we get:
w = (6 * sqrt10) / (5 * sqrt6)
Now, we can simplify further by multiplying numerator and denominator by sqrt6:
w = (6 * sqrt10 * sqrt6) / (5 * sqrt6 * sqrt6)
This simplifies to:
w = (6 * sqrt60) / (5 * 6)
The factor of 6 cancels out:
w = sqrt60 / 5
Finally, we can simplify sqrt60:
w = sqrt(4 * 15) / 5 = (2 * sqrt15) / 5
Therefore, the width of the rectangle is (2 * sqrt15) / 5 inches.