Question

The area of a square is 200cm^2. How long is the diagonal?

Answer 1

In order to solve this problem, we first need to find the side lengths of the square. We know that the area of a square is one length squared, so we can set up this equation:

200 =
`sidelength ^(2)`

We solve this by taking the square root of both sides.


`14.14 = sidelength`

So, one side of the square is 14.14cm. To finish this problem, we apply the pythagorean theorem. We can do this by drawing in the diagonal to make a triangle (shown in attachment - the blue part in the second drawing is the section that we use. Please note that the drawing is not to scale)

The pythagorean theorem is
`a^(2) + b^(2) = c^(2)`, where c squared is the diagonal of a right triangle. A squared and b squared are the other two sides. We can now plug in our numbers.


`14.14^(2) +14.14^2=c^2=20`

So, the diagonal length is 20 cm.