The length of diagonal of a square measure 10cm^2. What is the perimeter of the square? Express your answer in simplest radical form.
The side of the square = 10 / √2 cm = 5√2 cm
And the perimeter is 4 times this = 20√2 cm
Note that we can use the Pythagorean Theorem to find the diagonasl of a square
diagonal = sqrt (side^2 + side^2) = sqrt ( 2 * side^2) = side * sqrt (2)
So....the side = diagonal / sqrt (2)
So we have that the side = 10 / sqrt (2)
Multiply top/bottom by sqrt (2) and we get that
side = 10 sqrt (2) / [ sqrt (2) * sqrt (2) ] = 10 sqrt (2) / 2 = 5 sqrt (2)
We know a square has all 90 degree angles and equivalent side lengths, and the diagonal is \(10\sqrt2\).
So, you could make a right triangle, with two of the sides and the diagonal!
\(x^2+x^2=(10\sqrt2)^2\) so \(2x^2=200, x^2=100, x=10\)because x cannot be negative.
This is the side length of the square, so now just multiply it by four to get 40 cm.
You are very welcome!