Final answer:
The length of the diagonal of a rectangle with a length of 30 yards and a width of 40 yards is found using the Pythagorean theorem. It is calculated as the square root of the sum of the squares of the length and the width. The diagonal measures 50 yards.
Step-by-step explanation:
To find the length of the diagonal of a rectangle with a length of 30 yards and a width of 40 yards, you would use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides (the length and the width of the rectangle).
So, for your rectangle, the calculation would look like this:
- Diagonal2 = Length2 + Width2
- Diagonal2 = 302 + 402
- Diagonal2 = 900 + 1600
- Diagonal2 = 2500
- Diagonal = √2500
- Diagonal = 50 yards
Therefore, the length of the diagonal is 50 yards.