What is the approximate length of the diagonal of a square if the perimeter of the square is 12ft?
a. 1.7ft
b. 3.5ft
c. 4.2ft
d. 12.7ft
and how?I was confused on this question I tried to subtract and divide but nothing work.
Erin is wrong.
12/4 = 3
a^2 + b^2 = c^2
3^2 + 3^2 = c^2
9 + 9 = 18
What is the square root of 18?
To find the length of the diagonal of a square, we can use the Pythagorean Theorem.
Let's start by finding the length of one side of the square. Since the perimeter of the square is 12ft, and a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.
12ft ÷ 4 = 3ft
So, each side of the square is 3ft.
Now, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the square is the hypotenuse, and the two sides are the length of one side of the square (3ft).
So, we have:
diagonal^2 = side^2 + side^2
diagonal^2 = 3^2 + 3^2
diagonal^2 = 9 + 9
diagonal^2 = 18
To find the length of the diagonal, we take the square root of each side:
diagonal = √18
Using a calculator, the approximate value of √18 is 4.24ft.
So, the approximate length of the diagonal of the square is 4.24ft.
Based on the given options, the closest value is 4.2ft (option c).