A square has diagonal length 13 m. What is the side length of the square to the nearest centimeter?
Pitagorin teorem :
diagonal = sqrt ( a ^ 2 + a ^ 2 )
diagonal = sqrt ( 2 * a ^ 2 )
diagonal = a * sqrt ( 2 )
13 = a * sqrt ( 2 ) Divide both sides by aqrt ( 2 )
13 / sqrt ( 2 ) = a
13 / 1.41421 = a
9.19241131 = a
a = 9.19241131 m
1 m = 100 cm
a = 9.19241131 m = 919.241131 cm
a = 919 cm to the nearest centimeter?
To find the side length of the square, 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 this case, the diagonal of the square acts as the hypotenuse, and the two sides of the square are equal. Let's call the side length of the square "s".
Using the Pythagorean theorem, we have:
s^2 + s^2 = (13)^2
2s^2 = 169
Dividing both sides of the equation by 2, we get:
s^2 = 84.5
Taking the square root of both sides of the equation, we find:
s ≈ √(84.5)
s ≈ 9.19 m
To the nearest centimeter, the side length of the square is approximately 9.19 m.
To find the side length of the square, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the square is the hypotenuse of a right triangle, and the two sides of the triangle are the side lengths of the square.
Let's denote the side length of the square as 'x'. Then, using the Pythagorean theorem, we have:
x^2 + x^2 = 13^2
Simplifying this equation, we get:
2x^2 = 169
Dividing both sides of the equation by 2, we have:
x^2 = 84.5
To find x, we take the square root of both sides of the equation:
x = √84.5
Calculating the square root, we get:
x ≈ 9.2
Therefore, the side length of the square is approximately 9.2 meters.
But the question asks for the side length to the nearest centimeter, so we need to convert 9.2 meters to centimeters. Since 1 meter is equal to 100 centimeters, we can multiply the side length by 100:
side length (in centimeters) = 9.2 meters * 100 centimeters/meter
= 920 centimeters (rounded to the nearest centimeter)
Therefore, the side length of the square, to the nearest centimeter, is 920 centimeters.