The length of a diagonal of a square is 20 inches. what is its perimeter in radical form

Accepted Solution

The perimeter of the square is [tex]40\sqrt{2} in[/tex]Data;Diagonal = 20 inchesPerimeter = 4LPerimeter of a SquareThe perimeter of a square is given as 4 times the length of it's side length.[tex]P = 4L[/tex]Assuming the diagonal and two of it's side forms a right-angle triangle, we can use Pythagoras theorem and solve for it's side length.Given that[tex]x^2 = y^2 + z^2[/tex]where y and z = side length and equal L[tex]x^2 = y^2 + ^2\\20^2 = l^2 + l^2\\400 = 2l^2\\\frac{400}{2} = l^2\\200 = l^2\\\\l = \sqrt{200} \\l = 14.14in[/tex]The side length of the square is 14.14 inches.Using this information, let's find the perimeter of the square[tex]p = 4L\\p = 4 * 14.14\\p = 56.56in[/tex]But since we are asked to express our answer in radical form[tex]l = \sqrt{200}\\p = 4L\\p = 4*\sqrt{200}\\p = 40\sqrt{2} in[/tex]From the calculations above, the perimeter of the square is [tex]40\sqrt{2} in[/tex]Learn more on perimeter of a square here;