Question

The length of a diagonal of a square is 7V2 millimeters. Find the perimeter of the square.

a. 49 millimeters b. 2812 millimeters
c. 28 millimeters d. 98 millimeters

plz help it’s due today

Answer 1

The perimeter is c. 28 millimeters

Explanation:

The Perimeter of a Square

The perimeter of a square is the sum of all its side lengths. If the side length is L, then the perimeter is:

P = 4L

The diagonal of a square is the hypotenuse of a right triangle with both legs of length L.

Applying Pythagora's theorem, we find the length of the diagonal is:

`D=√(2)L`

We know the diagonal of a square is

`D=7√(2)`

We can find the side length L:

`√(2)L=7√(2)`

Simplifying:

L = 7 millimeters

Thus, the perimeter is:

P = 4*7 = 28

The perimeter is c. 28 millimeters