A square has side lengths of 5.7 m. If this square is stretched into a rectangle with sides of 5.7 m and 6.2 m, by what length has the diagonal increased?
0.4 cm
0.28 cm
0.63 cm
1.3 cm
To find the increase in length of the diagonal, we need to find the difference between the original diagonal and the new diagonal.
For the square with side length 5.7 m, the diagonal can be found using the Pythagorean theorem:
(diagonal)^2 = (side length)^2 + (side length)^2
(diagonal)^2 = 5.7^2 + 5.7^2
(diagonal)^2 = 32.49 + 32.49
(diagonal)^2 = 64.98
diagonal ≈ sqrt(64.98)
diagonal ≈ 8.08 m
For the rectangle with sides 5.7 m and 6.2 m, the diagonal can also be found using the Pythagorean theorem:
(diagonal)^2 = (side length)^2 + (side length)^2
(diagonal)^2 = 5.7^2 + 6.2^2
(diagonal)^2 = 32.49 + 38.44
(diagonal)^2 = 70.93
diagonal ≈ sqrt(70.93)
diagonal ≈ 8.43 m
To find the increase in the diagonal length, we subtract the original diagonal from the new diagonal:
Increase in diagonal = new diagonal - original diagonal
Increase in diagonal = 8.43 m - 8.08 m
Increase in diagonal ≈ 0.35 m
Since the side lengths were given in meters, the increase in diagonal length will also be in meters. Therefore, the increase in diagonal length is approximately 0.35 m or 35 cm.
None of the given answer choices are correct.