The perimeter of a square is 64 ft. Find the length of a diagonal. Please show me all the steps.
Just plug the numbers into the Pythagorean Theorem. You're looking for c.
a^2 + b^2 = c^2
is the answer is c=22.62 for problem the perimeter of a square is 64ft.find the length of a diagonal.
You're right!
To find the length of a diagonal of a square, we can use the Pythagorean theorem.
Step 1: Let's first find the length of one side of the square.
Since the perimeter of the square is 64 ft, and a square has four equal sides, we can divide the perimeter by 4 to get the length of one side.
64 ft ÷ 4 = 16 ft
Step 2: Now, let's use the Pythagorean theorem to find the length of the diagonal.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In a square, the diagonal forms a right triangle with two sides equal to the length of one side of the square.
Let's call the length of the diagonal "d".
Using the Pythagorean theorem, we have:
d^2 = a^2 + b^2
Since both sides of the square are equal in length, we can substitute the length of one side with "a" and "b".
Thus, we get:
d^2 = (16 ft)^2 + (16 ft)^2
Simplifying further:
d^2 = 256 ft^2 + 256 ft^2
d^2 = 512 ft^2
Step 3: To find the value of "d" (the length of the diagonal), we take the square root of both sides of the equation.
√(d^2) = √(512 ft^2)
d = √512 ft
Step 4: Simplifying the square root of 512:
d ≈ 22.63 ft
Therefore, the length of the diagonal of the square is approximately 22.63 ft.
I worked one out for you a few minutes ago.
http://www.jiskha.com/display.cgi?id=1335625629
I'll be glad to check your answer.