Find, to the nearest tenth of a centimeter, the length of a diagonal of a square if the measure of one side is 8.0 centimeters.
The diagonal of a square measures 12 feet.
a. What is the exact measure of a side of the square?
b. What is the area of the square
Pythagorean Theorem
a^2 + b^2 = c^2
8^2 + 8^2 = c^2
64 + 64 = c^2
11.3 = c
Use the Pythagorean Theorem.
What do you get for the measurement of a side of the square?
I manage to get X^2+X^2=144
Right so far.
2x^2 = 144
x^2 = 72
x = 8.4852813
Each side = 8.4852813 feet
A = s^2
A = 72 square feet
To find the length of a diagonal of a square, we can use the Pythagorean theorem, which states that in a right-angled 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, all sides have the same length, and each interior angle is 90 degrees, so we have a right-angled triangle. Let's denote the length of one side of the square as "s" and the length of the diagonal as "d".
Using the Pythagorean theorem, we have:
d^2 = s^2 + s^2
Since each side of the square is 8.0 centimeters, we can substitute this value:
d^2 = 8.0^2 + 8.0^2
d^2 = 64 + 64
d^2 = 128
To find the length of the diagonal, we can take the square root of both sides:
d = √128
Calculating the square root of 128, we find:
d ≈ 11.3 centimeters
Therefore, to the nearest tenth of a centimeter, the length of the diagonal of the square is approximately 11.3 centimeters.