A cube measures 5 cm on each side.
How long is the diagonal that connects two opposite
corners of the cube? Give an exact answer.
First, use the Pythagorean Theorem to find the length of the diagonal of one face of the cube.
a^2 + b^2 = c^2
25 + 25 = c^2
50 = c^2
7.0711 = c
That gives you another triangle with two sides >> 5 cm and 7.0711 cm
5^2 + 7.0711^2 = c^2
25 + 50 = c^2
75 = c^2
8.6603 = c
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http://mathcentral.uregina.ca/QQ/database/QQ.09.04/brett1.html
To find the length of the diagonal that connects two opposite corners of a cube, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the three sides of the right-angled triangle are the three edges of the cube. We need to find the length of the diagonal, which is the hypotenuse of the right-angled triangle.
Since all sides of the cube are equal and measure 5 cm, we can use this length as the length of the other two sides of the right-angled triangle. So, we have:
Side 1 = Side 2 = 5 cm
Using the Pythagorean theorem:
Diagonal^2 = Side 1^2 + Side 2^2
Diagonal^2 = 5^2 + 5^2
Diagonal^2 = 25 + 25
Diagonal^2 = 50
Taking the square root of both sides:
Diagonal = √50
Simplifying the square root:
Diagonal = √(25 * 2)
Diagonal = √25 * √2
Diagonal = 5√2 cm
Therefore, the length of the diagonal that connects two opposite corners of the cube is exactly 5√2 cm.