Find the perimeter of a square whose diagonal is 8 feet. round to the nearest tenth if needed.
math test tomorrow

Hello from MrBillDoesMath!

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

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

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