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) About Me  (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