the perimeter of a square is 36. what is the length of the diagonal?

Question

I need so help with this.

Answer 1

If the perimeter is 36 and it's a square, then the length of each side is 9. 4 x 9 = 36

Since it's a square, all the angles are right angles, so the diagonal, coupled with 2 sides, forms a right triangle with the diagonal as the hypotenuse.

In a right triangle, a^2+b^2=c^2, where c is the hypotenuse

In this case: 9^2+9^2=c^2 -> 81+81=c^2 ->162=c^2

c^2=162

c=the square root of 162, which simplifies into 9 x square root of 2.

Answer 2

Perimeter of a square = 4 times the side = 36 and so the side = 36/4 = 9 units

The length of the diagonal is like the hypotenuse of a right angled triangle where the two sides are equal and are at a right angle. So, we have diagonal = hypotenuse = sqrt[2 X side^2] = sqrt [2 X 81] = sqrt(162) = 12.7279 approx.

Answer 3

Well, you know that all 4 sides are equal. So, each one is 36/4 or 9. Then, draw a line between two opposite corners. That gives you two triangles with a right angle in one corner and with two sides of 9 each.

Now, just use Pythagorean Theory to find the length of the other side of the triangle - the hypotenuse (which is really the diagonal of the square).

Pyth. says... a^2 + b^2 = hypotenuse^2
9^2 + 9^2 = hypotenuse^2
81 + 81 = hypotenuse^2
162 = hypotenuse^2

So... the length is the square root of 162...

Answer 4

The perimeter of the square is 36units Hence each of its sides measures 36/4 or 9 units
therefore length of each of its diagonals is
square root(9^2+9^2)
= sqrt 162
=12.728 units

Answer 5

Perimeter of the a-length square is: P = 4a
and its area: A = a^2

If P = 36 = 4a,
then a = 36/4 = 9

Its length is then, 9

The angle (X) of right triangle formed is: 45 degrees.
cosX = cos(45) = sqrt(2)/2 = 1/sqrt(2)

length (a) = diagonal * cos(45) -->
diagonal = a / cos(45) =
= 9 / [ 1/sqrt(2) ] = 9 sqrt(2)
= 12.7279220613579

Also, d*d = a*a + b*b (From Pythagoras' Theorem),
but a = b = t, so
d*d = a*a + b*b = t*t + t*t = 2 * t *t -->
d^2 = 2 * t^2 -->
d = t * sqrt(2) = 9 * sqrt(2) = 12.7279220613579

And finally, its area (A) is:
A = a^2 = 9^2 = 81

Answer 6

The side length, s = 36/4 = 9.
Now s² + s² = d²,
where d is the diagonal length. This comes
from the Pythagorean theorem.
So d² = 2*9^2
d = 9*√2.

Answer 7

perimeter of a square is 4*Side

therefore, side = 36/4 = 9

diagonal of a square can be found by pythogarus theorem,

diagonal = root of ( 2 * 9^2)

diagonal = root of (162)

diagonal = 12.73

Answer 8

A square has four sides, so 36 divided by 4 is 9. Using the pathagorean theorum (a sqaured + b sqaured = c squared). 9 square plus 9 sqaure is 81 plus 81 which is 162. The sqaure root of 162 is approximatley 12.7...or 12.72792206. Thus, the diagonal, or hypotenuse of a sqaure with the permiter of 36 is 12.7

Answer 9

If the perimeter is 36, each side is 9

Using the Pythagorean theorem, determine the hypotenuse which is also the diagonal.

hyp^2 = 9^2 + 9^2
hyp^2 = 162
hyp = 162^0.5
hyp = 12.73

Answer 10

perimeter is 36.
so side will be 36/4=9.
two succesive sides will form right angle triangle.
using pythagorus theorem, diagonal is 9*square root of 2