what is the measure of one side of a square whose diagonal is 12cm?
Use Pythagorean Theorem.
s^2 + s^2 = 12^@
12^2
To find the measure of one side of a square given its diagonal, you can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In the case of a square, the diagonal acts as the hypotenuse.
In a square, all sides are equal, so let's assume the measure of one side is "x" cm.
By applying the Pythagorean Theorem, we can form the following equation:
x^2 + x^2 = (12 cm)^2
Simplifying this equation:
2x^2 = 144 cm^2
Dividing both sides of the equation by 2:
x^2 = 72 cm^2
Finally, taking the square root of both sides:
x = √72 cm
Simplifying the surd:
x ≈ 8.49 cm
Therefore, the measure of one side of the square is approximately 8.49 cm.