The length of a football pitch is 100m and the width of the pitch is 80 m calculate the length of a diagonal of the pitch give your answer to the nearest metre
If the diagonal is d, then
d^2 = 80^2 + 100^2
d = 20√41
To calculate the length of the diagonal of the pitch, you can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length and the width of the pitch form the two sides of the right-angled triangle, and the diagonal is the hypotenuse.
Let's label the length of the pitch as side A, the width as side B, and the diagonal as side C.
Given:
Length (A) = 100 m
Width (B) = 80 m
Using the Pythagorean theorem, we can write the equation:
A^2 + B^2 = C^2
Substituting the values:
(100 m)^2 + (80 m)^2 = C^2
Simplifying:
10,000 m^2 + 6,400 m^2 = C^2
16,400 m^2 = C^2
Taking the square root of both sides to solve for C:
C = √16,400 m^2
C ≈ 128 m (rounded to the nearest meter)
Therefore, the length of the diagonal of the football pitch is approximately 128 meters.