SOLUTION: the diagonal of square is 16 meters. what is its area in square meters?
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Question 563718: the diagonal of square is 16 meters. what is its area in square meters?
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
A square is equal on all 4 sides.
Let each side = x.
The diagonal and two sides form a right triangle.
We can use the Paythagorean Theorem to start with.
x^2 + x^2 = 16^2
2x^2 = 256
x^2 = 256/2
x^2 = 128
Take square root of both sides.
sqrt{x^2} = sqrt{128}^2
x = sqrt{64} * sqrt{2}
x = 8(sqrt{2})
Now that we know the value for x, we use A = (side)^2 to find the area.
A = [8(sqrt{2})]^2
A = 128m^2
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