Question

Find the perimeter of a square if the length of its diagonal is 14.

? square root of ?

Answer 1

28√2 units.

Explanation:

Let's denote the length of a side of the square as "s". We know that the diagonal of the square is √2 times the length of a side, so we can write:

√2 s = 14

Solving for "s", we can divide both sides by √2:

s = 14 / √2

To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √2:

s = (14 / √2) x (√2 / √2) = 14√2 / 2 = 7√2

Now we can find the perimeter of the square by adding up the lengths of all four sides:

Perimeter = 4s = 4(7√2) = 28√2

Therefore, the perimeter of the square is 28√2 units.