The length of a diagonal of a square is 24 square root two millimeters. find the perimeter of the square.
select one:
o a. 576 millimeters
o b.962 millimeters
c. 96 millimeters
d. 1152 millimeters
o

96 mm

Step-by-step explanation:

A square has 4 equal lengths. If you cut through with a diagonal, then you have form a right isosceles triangle.

So we have the diagonal, the hypotenuse, is mm.

We need to find the side measurement of the square, one of the leg measurements of the right isosceles triangle.

Let's assume it's leg measurement is x.

So by Pythagorean Theorem we have:

Combine like terms and simplify:

The square and square root cancel there.

I'm going to stick 24^2 * 2 in my calculator:

Divide both sides by 2:

Take the square root of both sides:

So each side of the square is 24 mm long.

To find the perimeter I add up add all the side measurements of the square or multiply 24 by 4 since all sides of square are congruent.

24(4)=96

Answer is 96 mm

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet