Question

A square has side lengths of 5.9 m. If this square is stretched into a rectangle with sides of 5.9 m and 6.4 m by what length has the diagonal increased?

a. 0.28 cm

c. 0.63 cm

b. 0.4 cm

d. 1.3 cm

Answer 1

To find the increase in the diagonal, we need to compare the diagonals of the square and the rectangle.

In a square, the diagonal is found using the Pythagorean theorem: diagonal^2 = side^2 + side^2

For a square with side length 5.9 m, the diagonal is:

diagonal_square^2 = 5.9^2 + 5.9^2
diagonal_square^2 = 2(5.9^2)
diagonal_square = √(2(5.9^2))
diagonal_square ≈ 8.352 m

In the rectangle, the diagonal can also be found using the Pythagorean theorem: diagonal^2 = side^2 + side^2

For a rectangle with sides 5.9 m and 6.4 m, the diagonal is:

diagonal_rectangle^2 = 5.9^2 + 6.4^2
diagonal_rectangle^2 = 5.9^2 + (1.5 × 5.9)^2
diagonal_rectangle^2 = 5.9^2 + (1.5^2 × 5.9^2)
diagonal_rectangle^2 = (1 + 1.5^2) × 5.9^2
diagonal_rectangle^2 = 5.225 × 5.9^2
diagonal_rectangle = √(5.225 × 5.9^2)
diagonal_rectangle ≈ 9.202 m

The increase in the diagonal is therefore:

increase = diagonal_rectangle - diagonal_square
increase = 9.202 m - 8.352 m
increase ≈ 0.85 m

However, none of the answer choices are measured in meters. Therefore, we must convert the increase to centimeters:

increase = 0.85 m × 100 cm/m
increase ≈ 85 cm

The closest answer choice to 85 cm is 0.63 cm. Therefore, the correct answer is c. 0.63 cm.