The area of a square garden 300 m^2. How long is the diagonal?
a. 5√6m
b. 150m
c. 10√6 m
d. 900 m
To find the diagonal of the square garden, we need to use the Pythagorean Theorem which states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides. In this case, the two sides are the lengths of the garden's sides, which are equal since it is a square.
Let's call the length of each side "s". We know that the area of the square is 300 m^2, so:
s^2 = 300
Taking the square root of both sides, we find:
s = √300 = 10√3
Now we can use the Pythagorean Theorem:
(diagonal)^2 = s^2 + s^2
(diagonal)^2 = 2s^2
(diagonal)^2 = 2(10√3)^2
(diagonal)^2 = 2(300)
(diagonal)^2 = 600
(diagonal) = √600 = 10√6
Therefore, the answer is c. 10√6 m.