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?
Let's call the length of one side of the square "x".
According to the Pythagorean theorem, the length of the diagonal of a square with side length x is given by √(x^2 + x^2) = √(2x^2) = x√2.
Since the length of the diagonal is given as 7 inches, we have the equation x√2 = 7.
To find the actual length, we can isolate x by dividing both sides of the equation by √2: x = 7 / √2.
Rationalizing the denominator (multiplying by √2/√2), we get x = 7√2 / 2.
To the nearest whole number, the length of the diagonal of the square would be the nearest whole number to x, which is 3.
Therefore, the actual length, in inches, of the diagonal of the square could be 3 inches.
To find the actual length of the diagonal of the square, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In a square, the diagonal is the hypotenuse of a right-angled triangle formed by two sides of the square. Let's call the length of each side of the square "x".
According to the Pythagorean theorem, the equation would be:
x^2 + x^2 = 7^2
Simplifying the equation:
2x^2 = 49
Dividing both sides by 2:
x^2 = 24.5
Taking the square root of both sides to find x:
x ≈ 4.95
Since we need to find the nearest whole number, the possible actual length of the diagonal of the square could be either 5 inches or 4 inches.