Final answer:
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. In this case, the length of the rectangle is 120 meters and the width is 90 meters. Using the Pythagorean theorem, the length of the diagonal is found to be 150 meters.
Step-by-step explanation:
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of the rectangle is 120 meters and the width is 90 meters.
We can consider the length as one side of the right triangle and the width as the other side. Let's call the diagonal 'd', the length 'l', and the width 'w'.
Using the Pythagorean theorem, we have the equation: d^2 = l^2 + w^2.
Substituting the values, we get: d^2 = 120^2 + 90^2.
Simplifying, we have: d^2 = 14400 + 8100.
Calculating: d^2 = 22500.
Taking the square root of both sides: d = √22500.
Calculating: d = 150.
Therefore, the length of the diagonal of the soccer field is 150 meters. So the correct answer is option a) 150 meters.