Question

Find the perimeter of a square whose diagonal is 8 feet. Round to the nearest tenth if needed.​

Answer 1

Hello from MrBillDoesMath!

Answer:

22.6

Discussion:

From the attachment, the square has sides of length "x", and the Pythagorean theorem applies. Hence

x^2 + x^2 = 8^2           =>

2 x^2 = 8^2                 => divide both sides by 4

x^2   = 8^2/2               => 8^2 = 64,   8^2/2 = 32

x^2 = 32                      =>

x = sqrt(32) =               => as 32 = 16 * 2

x = sqrt(16) *  sqrt(2)    =>

x = 4 sqrt(2)

The perimeter is 4*x

             = 4*(4 sqrt(2) )

             = 16 * sqrt(2)        => as sqrt(2) is approx 1.41

            = 22.6

Thank you,

MrB