Answer:
The length of the diagonal of a square can be found by using the Pythagorean theorem. 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, the two sides that form the right angle are equal in length, so we can call each side "s." The length of the diagonal, which acts as the hypotenuse, can be represented as "d."
Using the Pythagorean theorem, we can write the equation as:
d^2 = s^2 + s^2
Simplifying the equation, we get:
d^2 = 2s^2
To find the length of the diagonal, we need to solve for "d." Since the problem tells us that the length of the diagonal is 7 inches, we can substitute that value into the equation:
7^2 = 2s^2
49 = 2s^2
Dividing both sides by 2, we get:
24.5 = s^2
Now, we need to find the square root of 24.5 to find the length of each side, which is also the length of the diagonal.
Calculating the square root of 24.5, we find:
√24.5 ≈ 4.9497
Rounding this value to the nearest whole number, we get:
The length of the diagonal is approximately 5 inches.
Now let's look at the given options: /40, √13, √50, and √21.
Calculating the square root of each option:
√13 ≈ 3.6056
√50 ≈ 7.0711
√21 ≈ 4.5826
The only option that is closest to 5 inches is √21.
Therefore, √21 could be the actual length, in inches, of the diagonal of the square.
Explanation:
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