Question

Find the perimeter of a square with the diagonal of 2 inches.2√16 in08 inΟ 2 inO 4√2 in2 in

Answer 1

We need to find the perimeter of the square using the given diagonal:

If we look at the diagonal, it represents the hypotenuse of a right triangle.

Now, we can use the Pythagorean theorem to find the other sides.

`h^2=a^2+b^2`

Where h represents the hypotenuse.

a and b represent the other sides

If the square has all sides with the same measure, we can replace using the function:

Then, solve for x

(x represents a side of the triangle)

`\begin{gathered} 2^2=x^2+x^2 \\ 4=2x^2 \\ (4)/(2)=x^2 \\ 2=x^2 \\ √(2)=x \end{gathered}`

Finally, the perimeter of a triangle is given by the sum of all the sides. (a square has 4 sides)

Then,

Perimeter = √2+√2+√2+√2 = 4√2

Hence, the correct answer is the last option.