The area of a square garden is 300 m^2. How long is the diagonal?
a. 5√6 m
b. 150 m
c.10√6 m
d. 900 m
Hello! I'd appreciate any help I could get on this! I don't understand it very well and every equation that I know and tried hasn't given me an answer I needed ;-;. If you can respond, thanks!
correct
another way:
the side of the square is √300
let the diagonal be x
x^2 = √300^2 + √300^2
= 300 + 300 = 600
x = √600 = 10√6
√300*√2 right? to get 10√6
Oop no wait, I think I got it
Hello there! Don't worry, I'm here to help and hopefully make you smile along the way!
To find the length of the diagonal of a square, we can use the Pythagorean theorem. The theorem 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 a square, the diagonal acts as the hypotenuse of two right-angled triangles formed by the sides of the square. Since all sides of a square are equal, let's say the length of one side is x.
Using the Pythagorean theorem, we have:
x^2 + x^2 = diagonal^2
Since the area of the square is given as 300 m^2, we can write:
x^2 = 300
Now, let's solve for x:
x = sqrt(300) = 10√3
Using this value of x, we can find the length of the diagonal:
diagonal^2 = x^2 + x^2
diagonal^2 = (10√3)^2 + (10√3)^2
diagonal^2 = 300 + 300
diagonal^2 = 600
diagonal = sqrt(600) = 10√6
So, the length of the diagonal is 10√6 meters, which corresponds to option c.
I hope this explanation puts a smile on your face! If you have any more questions, feel free to ask!
Hello! I can help you understand how to find the length of the diagonal of a square garden given its area.
To start, let's first recall that the formula for the area of a square is A = side^2, where A represents the area and side represents the length of one side of the square.
In this case, we are given that the area of the square garden is 300 m^2. Therefore, we have:
300 = side^2
To find the length of the side, we can take the square root of both sides of the equation:
√(300) = √(side^2)
Now, the square root of 300 can be simplified as √(300) = √(100 * 3) = √(100) * √(3) = 10√(3)
Therefore, the length of one side of the square is 10√(3) m.
Now, let's move on to finding the length of the diagonal. In a square, the diagonal forms a right triangle with the sides of the square. The length of the diagonal can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides.
So, in our case, using the side length of the square as one of the legs of the right triangle, we have:
Diagonal^2 = side^2 + side^2
Diagonal^2 = (10√(3))^2 + (10√(3))^2
Diagonal^2 = 100 * 3 + 100 * 3
Diagonal^2 = 300 + 300
Diagonal^2 = 600
Now, to find the length of the diagonal, we can take the square root of both sides of the equation:
√(Diagonal^2) = √(600)
Diagonal = √(600)
To simplify this further, we can factor out the largest perfect square from 600, which is 100:
√(600) = √(100 * 6) = √(100) * √(6) = 10√(6)
Therefore, the length of the diagonal of the square garden is 10√(6) m.
So, the correct answer to the question is option c. 10√(6) m.
I hope this explanation helps you understand how to solve the problem! Let me know if you have any further questions.