Question

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

Answer 1

The perimeter of the square is $40\sqrt{2} in$

Data;

• Diagonal = 20 inches
• Perimeter = 4L

Perimeter of a Square

The perimeter of a square is given as 4 times the length of it's side length.

$P = 4L$

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

$x^2 = y^2 + z^2$

where y and z = side length and equal L

$x^2 = y^2 + ^2\\20^2 = l^2 + l^2\\400 = 2l^2\\\frac{400}{2} = l^2\\200 = l^2\\\\l = \sqrt{200} \\l = 14.14in$

The side length of the square is 14.14 inches.

Using this information, let's find the perimeter of the square

$p = 4L\\p = 4 * 14.14\\p = 56.56in$

But since we are asked to express our answer in radical form

$l = \sqrt{200}\\p = 4L\\p = 4*\sqrt{200}\\p = 40\sqrt{2} in$

From the calculations above, the perimeter of the square is $40\sqrt{2} in$

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