Answer :
Answer:
length of x is 50 yards
Step-by-step explanation:
Pythagorean Theorem: a^2 + b^2 = c^2
30^2 + 40^2 = c^2
900 + 1600 = c^2
2500 = c^2 need to solve for c, square root both sides
50 = c
The length of the diagonal is 50 yards. The diagonal of a rectangle divides the rectangle into two right-angled triangles. Thus, by applying the Pythagoras theorem we can able to find the length of the diagonal.
What is the Pythagoras theorem?
The theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) and the algebraic notation, [tex]a^2 + b^2 = c^2[/tex].
Finding the diagonal of the rectangle:
The diagonal of a rectangle divides the rectangle into two halves of right-angled triangles.
The length and breadth of the rectangle are 40 yards and 30 yards.
The diagonal x divides the rectangle. So, it becomes a common hypotenus for the two right-angled triangles.
So, applying the Pythagoras theorem.
x^2 = (40)^2 + (30)^2
= 1600 + 900
= 2500
Thus, the value of x is 50 yards.
Therefore, the length of the diagonal is 50 yards.
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