Question

Calculate the perimeter of a square whose diagonal measures 29 dm.

Answer 1

Answer:

$4\sqrt{420.5}$ dm

Step-by-step explanation:

A square's diagonal cuts across the square, making two right triangles where the diagonal is the hypotenuse.

We have a right triangle with a hypotenuse of 29, and two legs that are the same length (because they are sides of a square)

So, we can use pythagoreans theorem to find the lengths of the legs, or sides of the square.

$a^2 + a^2 = 29^2$

$2a^2 = 841$

$a^2 = 420.5$

$a = \sqrt{420.5}$

Now that we have a side length of $\sqrt{420.5}$, we just have to multiply that by 4, since a square has 4 sides. This leaves us with a final perimeter of:

$4\sqrt{420.5}$