Question

Given: √24 Ft, B = 2√34

a. Perimeter
b. Area
Determine if the perimeter and area answers are rational or irrational and explain why.

Answer 1

The perimeter of the square is 8√6 feet, which is irrational, and the area is 24 square feet, which is rational. The perimeter is irrational due to the square root of a non-perfect square, and the area is rational as it is an integer.

Step-by-step explanation:

The student has provided the side length of a square (√24 Ft), and a coefficient (B = 2√34) which seems unrelated to the given length. To find the perimeter (P) of the square, we multiply the side length by 4: P = 4(√24) Ft. Simplifying inside the radical gives P = 4(√(4 × 6)) Ft, which further simplifies to P = 4(2√6) Ft = 8√6 Ft.

For the area (A), we square the side length: A = (√24) Ft × (√24) Ft = 24 Ft².

Both the perimeter and the area are irrational numbers. The perimeter is irrational because the square root of 6 is an irrational number. The area is rational because it is a product of an integer by itself, resulting in another integer.