If the length of a diagonal of a square is 15 cm, how long is each side?

Answer 1

[04]
We know that the diagonal of swuare
=sqrt2a^2,where a is the length of each side of the square
Therefore
sqrt 2a^2=15
2a^2=225
a^2=225/2
a=sqrt(225/2)=15/sqrt2=15 sqrt2/2 cm

Answer 2

Hey there!

If you divide the square into two triangles, you get a triangle measuring 45-45-90 degrees each.

This is useful, since now we can apply the 45-45-90 triangle theorem.

The 45-45-90 triangle theorem states that the hypotenuse of the triangle is sqrt(2) times more than each of the legs.

Well, we know the hypotenuse is 15.

So, applying the 45-45-90 triangle theorem, we get.

l*sqrt(2)=h -->
l*sqrt(2)=15 -->
l=15/sqrt(2)

So the length of each side is 15/sqrt(2) or 10.6 cm.

Hope it helps!

Answer 3

when a diagonal is drawn through a square, it's divided into two 45-45-90 triangles.

if you know the hypotenuse is 15, then you know the length of each leg is 15 divided by the square root of two. 15/sqrt2 simplifies into 15 times the squareroot of 2 over 2

15sqrt2/2

Answer 4

Pythagorean theorem:

a^2 + b^2 = c^2 where c is the hypotenuse.

A diagonal of a square is a hypotenuse of a right triangle...

2s^2 = 15^2
2s^2 = 225
s^2 = 225/2
s = 10.6066

Hope this helps!

Answer 5

Diagonal = Hypotenuse = 15
Find sides A and B since it is a square, these sides are equal
A^2+B^2 = 15^2 A^2+B^2 = 225 since sides are equal....
A^2 = 225/2 = 112.5 = 10.607 and B also equal 10.607

Proof:
10.607^2 + 10.607^2 = 15^2
112.5 + 112.5 = 225
225 = 225

Answer 6

for a given square : if each side = x ==> length of diagonal = x*sqrt(2). ==> 15=x*sqrt(2) ==> x=5/sqrt(2)=10.607 cm

Answer 7

Let side be x cm
x² + x² = 15²
2x² = 225
x² = 225 / 2
x = (1/√2) 15 cm
x = 10.6 cm (to 1 dec. place)

Answer 8

Let the sides of the square be denoted by x.
By Pythogorean theorem, x^2+x^2=15
2x^2=15
x^2=7.5
x=sqrt(7.5) each side

Answer 9

i dropped out of college but heres your answer
7.5 cm.

Answer 10

break it into a triangle. =]