The diagonal of a square is 3 feet long. Find its perimeter.
My answer:
a^2+b^2=c^2
x^2+x^2=3^3
2x^2=9 divide both side by 2
x^2=4.5
x=√4.5
x=2.1 feet
Is this right?
Obviously the perimeter cannot be shorter than one of its sides.
2.1 is the length of each of its sides.
Now find the perimeter.
how can the perimeter be less than the diagonal?
you found one of the sides...the perimeter is all four
Your answer is partially correct. However, there seems to be a mistake in your calculation. Let me guide you through the correct steps to find the answer to this problem.
To find the perimeter of a square with a given diagonal, we need to first find the length of one side of the square. Let's call this length "s".
In a square, each side is equal in length. Therefore, we can use the Pythagorean theorem to relate the diagonal length to the side length of the square:
s^2 + s^2 = c^2
Here, "c" represents the length of the diagonal, which in this case is 3 feet.
Since we have two identical terms in our equation, we simplify it to:
2s^2 = 3^2
2s^2 = 9
Next, we divide both sides of the equation by 2:
s^2 = 4.5
To find the value of "s," we take the square root of both sides of the equation:
√(s^2) = √4.5
s = √4.5
Now, let's calculate the value of "s" correctly:
s ≈ 2.12 feet (rounded to two decimal places)
Now that we have the correct value for "s," we can find the perimeter of the square. The perimeter of a square is found by multiplying the side length by 4:
Perimeter = 4s
Perimeter = 4(2.12) ≈ 8.46 feet (rounded to two decimal places)
Therefore, the correct answer is approximately 8.46 feet.