Find the length of each side of a square if the diagonal is 7(square root 2)?
How do I solve or set up this problem?
d = square root ( a ^ 2 + a ^ 2 )
d = square root ( 2 a ^ 2 )
d = square root ( 2 ) * square root ( a ^ 2 )
d = square root ( 2 ) * a
7 square root ( 2 ) = square root ( 2 ) * a Divide both sides by square root ( 2 )
7 = a
a = 7
Can you please explain that a little better, I am having a hard time understanding what you are saying
Bosnian is simply using the Pythagorean Theorem , where he called each of the sides a and the diagonal d
d^2 = a^2 + a^2
2a^2 = d^2
2a^2 = (7√2)^2 = 98
a^2 = 49
a = 7
Thank you
To find the length of each side of a square when given the length of its diagonal, you can set up and solve a equation using the Pythagorean theorem.
Let's assume that the length of each side of the square is "x". The diagonal of a square forms a right triangle with two sides that are congruent to the sides of the square. The diagonal acts as the hypotenuse of this right triangle.
According to the Pythagorean theorem, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides (sides of the square).
Applying this to our problem, we can write the equation as:
x^2 + x^2 = (7√2)^2
Simplifying the equation, we have:
2x^2 = 49 * 2
Dividing both sides of the equation by 2, we get:
x^2 = 49
Taking the square root of both sides, we have:
x = √49
Therefore, the length of each side of the square is 7.
So, the length of each side of the square is 7.