Final answer:
Dillan's sandbox is 12 feet wide and 4 feet long, and the diagonal measurement is found using the Pythagorean theorem. The calculation shows that the diagonal of the sandbox is approximately 12.65 feet.
Step-by-step explanation:
Dillan is building a rectangular sandbox that is 12 feet wide and 4 feet long, and he needs to find the diagonal measurement of the sandbox. To find the diagonal, we can apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the width and the length of the sandbox are the two other sides.
The formula we use is a2 + b2 = c2, where 'c' represents the diagonal. If we plug in the dimensions for the sandbox, we get:
12 ft2 + 4 ft2 = c2
144 ft2 + 16 ft2 = c2
160 ft2 = c2
Taking the square root of both sides of the equation to solve for 'c', we find that:
√160 ft2 ≈ 12.65 ft
So, the diagonal measurement of the sandbox is approximately 12.65 feet.