Find the side of a square whose diagonal is 16√2cm
Use Pythagorean theorem to find the value of a.
a² + b² = c²
The diagonal is the hypotenuse c.
Since a and b are equal, we consider them as a.
a² + a² = c²
2 a² = c²
2 a² = ( 16√2 )²
2 a² = 16² ∙ ( √2 )²
2 a² = 16² ∙ 2
Divide both sides by 2
a² = 16²
a = √16²
a = 16 cm
well, the diagonal of a square of side s is s√2, so what do you think?
To find the side length of a square when the diagonal is given, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In the case of a square with a diagonal, the diagonal is the hypotenuse and the sides of the square are the other two sides.
Let "s" be the side length of the square, and "d" be the length of the diagonal. The Pythagorean theorem equation for this scenario can be written as:
s^2 + s^2 = d^2
Simplifying the equation:
2s^2 = d^2
Dividing both sides of the equation by 2:
s^2 = d^2 / 2
Taking the square root of both sides:
s = √(d^2 / 2)
Given that the diagonal (d) is 16√2 cm, we substitute this value into the equation:
s = √((16√2)^2 / 2)
s = √(256 * 2 / 2)
s = √(512 / 2)
s = √256
s = 16 cm
Therefore, the side length of the square is 16 cm.
To find the side length 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 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 are the sides of the square. Let's call the side length of the square "s."
Using the Pythagorean theorem, we have the equation:
s^2 + s^2 = (16√2)^2
Simplifying the equation:
2s^2 = 256 * 2
2s^2 = 512
Now, divide both sides of the equation by 2:
s^2 = 512 / 2
s^2 = 256
To find the value of "s," take the square root of both sides:
√(s^2) = √256
s = 16
Therefore, the side length of the square is 16 cm.