Question
What is the length of the diagonal of the rectangle? 4x 8y
Answers
GPT 3.5
To find the length of the diagonal of a rectangle, 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 length of the rectangle is 4x and the width is 8y. Let's label the length as a and the width as b.
Therefore, a = 4x and b = 8y.
Using the Pythagorean theorem, the length of the diagonal (d) can be found as follows:
d^2 = a^2 + b^2
Substituting the values of a and b:
d^2 = (4x)^2 + (8y)^2
d^2 = 16x^2 + 64y^2
Taking the square root of both sides:
d = √(16x^2 + 64y^2)
Thus, the length of the diagonal of the rectangle is √(16x^2 + 64y^2).
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 length of the rectangle is 4x and the width is 8y. Let's label the length as a and the width as b.
Therefore, a = 4x and b = 8y.
Using the Pythagorean theorem, the length of the diagonal (d) can be found as follows:
d^2 = a^2 + b^2
Substituting the values of a and b:
d^2 = (4x)^2 + (8y)^2
d^2 = 16x^2 + 64y^2
Taking the square root of both sides:
d = √(16x^2 + 64y^2)
Thus, the length of the diagonal of the rectangle is √(16x^2 + 64y^2).