Final answer:
To determine the width of the rectangle, use the area formula: Area = length × width. After simplifying the square roots in the area and length expressions, divide the area by the length to find the width. The rectangle's width is calculated to be 30 inches.
Step-by-step explanation:
To find the width of the rectangle, we need to use the formula for the area of a rectangle, which is Area = length × width. The area of the rectangle is given as 30√3750 square inches, and the length is given as 3√250 inches. Now, we can set up the equation to solve for the width:
30√3750 = 3√250 × width
Simplifying the square roots before multiplying:
√3750 = √(750 × 5) = √750 × √5 = 15√5
√250 = √(50 × 5) = √50 × √5 = 5√5
Now substitute back into the area formula:
30(15√5) = 3(5√5) × width
We simplify by dividing both sides by the length, which is 3(5√5):
width = 30(15√5) / 3(5√5)
Cancel out common factors:
width = (30/3)(15/5)
width = 10 × 3
width = 30 inches
Therefore, the width of the rectangle is 30 inches.