to the nearest whole number, the length of the diagonal of a square is 7 inches. which measure could be the actual length, in inches, of the diagonal of the square?
responses
sqrt(13)
sqrt(40)
sqrt(21)
sqrt(50)
To find the actual length of the diagonal of the square, we need to square each of the given values and see if they equal 49 (7 squared).
- sqrt(13) ≈ 3.6 (when squared, ≈ 12.96)
- sqrt(40) ≈ 6.3 (when squared, ≈ 39.69)
- sqrt(21) ≈ 4.6 (when squared, ≈ 21.16)
- sqrt(50) ≈ 7.1 (when squared, ≈ 50.41)
Therefore, the nearest whole number length that could be the actual diagonal length is 7 inches, making the correct measure sqrt(50).
To find the actual length of the diagonal of the square, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
Let's call the length of one side of the square "x". According to the problem, the length of the diagonal (hypotenuse) of the square is 7 inches.
Applying the Pythagorean theorem, we have:
x^2 + x^2 = 7^2
2x^2 = 49
x^2 = 49/2
x^2 ≈ 24.5
We need to find the square root of 24.5 to find the length of one side, which will give us the length of the diagonal:
sqrt(24.5) ≈ 4.95
Thus, the actual length of the diagonal of the square is approximately 4.95 inches.
None of the given measures (sqrt(13), sqrt(40), sqrt(21), sqrt(50)) match our result of approximately 4.95 inches.