SOLUTION: Can you please help me out with this sum, i'm a little confused on how to do it...thank you in advance :)) A square has diagonals of length 10 cm. find the sides of the square.

Question 1171698: Can you please help me out with this sum, i'm a little confused on how to do it...thank you in advance :))
A square has diagonals of length 10 cm. find the sides of the square.
Found 2 solutions by math_tutor2020, math_helper:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x = side length of the square
Any square has all four sides the same length, so each side is x centimeters long.
It doesn't make sense to have x be negative, so we'll say x > 0.

Draw a square with one diagonal only. We have the square divided into two congruent right triangles. Focus on one of those right triangles.

This right triangle has congruent legs (x cm each) and a hypotenuse that is 10 cm long.
We'll let
a = x
b = x
c = 10
which will be plugged into the Pythagorean theorem to solve for x.

a^2 + b^2 = c^2
x^2 + x^2 = 10^2
2x^2 = 100
x^2 = 100/2
x^2 = 50
x = sqrt(50) .... applying the square root, keep in mind that x > 0
x = sqrt(25*2)
x = sqrt(25)*sqrt(2)
x = 5*sqrt(2)

Each leg is exactly 5*sqrt(2) cm long

Therefore, each side of the square is 5*sqrt(2) cm long.

This is known as the exact answer because we don't have any decimal approximations going on.

Use of your calculator should lead to the rough approximation of
5*sqrt(2) = 7.0710678
Note that
sqrt(50) = 7.0710678
to help confirm that sqrt(50) = 5*sqrt(2)

----------------------------------------------

Exact Answer: 5*sqrt(2) cm
Approximate Answer: 7.0710678 cm

Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

Refer to picture below.

From the Pythagorean Theorem,

cm or about 7.07cm

NOTE that the side length of a square is related to its diagonal length
by : diagonal_length = * side_length. Try
it out with a calculator, or better, derive it from the picture.

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