A rectangular hockey field is 50 m long and 35 m wide
calculate the length of its diagonal
Answers
If we draw a diagonal of a rectangle, we realize that we have actually divided the rectangle into two triangles. The angles of the rectangle all measure 90°. We can say that the length of the diagonal and the hypotenuse of the triangles the rectangle was divided into are same.
In this question, we find the length of the diagonal using the Pythagoras Theorem, which states that in a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
Given:
- The length of the rectangular hockey field = 50 m
- The width of the rectangular hockey field = 35 m
To find:
The length of its diagonal
Answer:
⇨ We know that h² = side² + side² (Pythagoras Theorem).
⇨ The measures of the two legs of the triangle are the length and the width of the hockey field.
⇨ So,
- 50² + 35² = h²
- 2500 + 1225 = h²
- 3725 = h²
- √3725 = h
⇨ The prime factorization of 3725 :
3725 = 5 x 5 x 149
3725 = 5² x 149
⇨ Since there is no pair for the prime number 149, 3725 is a non square number. Approximately, √3725 is equal to 61 m. We take 61 m as the approximate length of the diagonal of the rectangle and we are done :D
Thus, the length of the diagonal of the rectangular field is approximately 61 m.