(1 point)
Apply the Pythagorean Theorem to find the length of the diagonal of the square Round your answer to the nearest hundredth, if necessary
04.24
O283
To find the length of the diagonal of the square, we can use the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the length of the diagonal, and a and b are the lengths of the sides of the square.
In this case, the length of the sides of the square is 04.24. So, plugging this value into the equation, we get:
c^2 = (04.24)^2 + (04.24)^2
Simplifying, we have:
c^2 = 17.9776 + 17.9776
c^2 = 35.9552
Taking the square root of both sides to solve for c, we get:
c = √35.9552
Rounding to the nearest hundredth, the length of the diagonal is approximately 5.99.
To find the length of the diagonal of a square using the Pythagorean Theorem, you can use the formula:
d = √(s^2 + s^2)
Where d represents the length of the diagonal and s represents the length of one side of the square.
In this case, s = 4.24 (given), so we can substitute this value into the formula:
d = √(4.24^2 + 4.24^2)
d = √(17.9776 + 17.9776)
d = √35.9552
Using a calculator or rounding to the nearest hundredth, the length of the diagonal is approximately 5.99.
To apply the Pythagorean Theorem to find the length of the diagonal of a square, we need to know the length of one of its sides. 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 other two sides.
In the case of a square, all four sides are equal in length. So, if we have the length of one side, we can find the length of the diagonal.
In this case, the length of one side of the square is given as 4.24.
Let's call the length of the diagonal "d". We can set up the Pythagorean equation as follows:
d^2 = 4.24^2 + 4.24^2
Simplifying, we have:
d^2 = 17.9776 + 17.9776
d^2 = 35.9552
To find "d", we take the square root of both sides of the equation:
d = √35.9552
Calculating the square root using a calculator, we get d ≈ 6.00.
Rounding this answer to the nearest hundredth, we have the length of the diagonal as approximately 6.00 units.