A square is 7 meters on a side. To the nearest tenth of a meter, how long is the diagonal of the square?

A: 9.8
B: 9.9
C: 10.0
D: 14.0

The diagonal of a square forms two

45-45-90 triangles.

The sides of a 45-45-90 triangle are in the ratio,
a : b : hypotenuse
x : x : x(sqrt(2))

The diagonal is the hypotenuse of this 45-45-90 triangle.

Side = 7
7 * (sqrt(2)) = ?

a^2 + b^2 = c^2

7^2 + 7^2 = c^2
49 + 49 = 98

c = square root of 98

Be sure to round to the nearest tenth.

To find the length of the diagonal of a square, we can use the Pythagorean theorem, which states that in a right-angled 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 this case, the sides of the square are 7 meters each, so we can use them as the other two sides of the right-angled triangle formed by the diagonal.

Let's call the diagonal length d. By using the Pythagorean theorem, we have:

d^2 = 7^2 + 7^2
d^2 = 49 + 49
d^2 = 98

To find the length of the diagonal, we need to take the square root of both sides:

d = sqrt(98)
d ≈ 9.899

Rounding to the nearest tenth, the length of the diagonal is approximately 9.9 meters.

Therefore, the correct answer is B: 9.9 meters.