What is the length of the diagonal of a square with side lengths
7 sqrt of 2
To find the length of the diagonal of a square with side length \(7 \sqrt{2}\), we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In a square, the diagonal forms the hypotenuse of a right triangle with two sides being the sides of the square.
Let's call the length of the diagonal \(d\).
According to the Pythagorean theorem:
\((7 \sqrt{2})^2 + (7 \sqrt{2})^2 = d^2\)
Simplifying:
\(98 + 98 = d^2\)
\(196 = d^2\)
To find \(d\), we take the square root of both sides:
\(d = \sqrt{196}\)
Since \(\sqrt{196}\) is equal to 14, the length of the diagonal of the square is 14.
To find the length of the diagonal of a square, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In a square, the diagonals are the hypotenuses of two right triangles formed by the sides of the square. Since all sides of a square are equal, the two right triangles formed are congruent.
Let's label the side length of the square as "s". In this case, "s" equals 7 times the square root of 2.
Therefore, s = 7√2.
Using the Pythagorean theorem, we can calculate the length of the diagonal (d) as follows:
d^2 = s^2 + s^2
d^2 = (7√2)^2 + (7√2)^2
d^2 = 49 * 2 + 49 * 2
d^2 = 98 + 98
d^2 = 196
To find the length of the diagonal, take the square root of both sides:
d = √196
d = 14
Therefore, the length of the diagonal of a square with side lengths of 7√2 is 14 units.
d^2 = (7√2)^2 + (7√2)^2
= 98+98
= 196
d = √196 = 14