Final answer:
The perimeter of a rectangle with a length of 2√3 and a width of 4√75 is 44√3 after simplifying the width from 4√75 to 20√3 and applying the perimeter formula P = 2l + 2w.
Step-by-step explanation:
The student has asked how to find the perimeter of a rectangle with given length and width dimensions.
The formula to find the perimeter of a rectangle is
P = 2l + 2w,
where l is the length and w is the width of the rectangle.
To answer the student's question:
- First, we simplify the width of the rectangle.
- The width is given as 4√75.
- We can simplify this by recognizing that 75 is 25 times 3, and √25 is 5, so √75 is √25 * √3, which is 5√3.
- Therefore, the width is 4 * 5√3, which simplifies to 20√3.
- Now, we can calculate the perimeter by using the given length of 2√3 and the simplified width of 20√3.
- So the perimeter formula becomes P = 2(2√3) + 2(20√3), which is P = 4√3 + 40√3 = 44√3.
This is the perimeter of the rectangle in simplest radical form.