A lined napkin,in the shape of a square,has sides 9-inches long.if the napkin is folded along the diagonal,what is the length of the diagonal ?
9^2 + 9^2 = c^2
Solve for c.
Well, we can't have any crooked lines when it comes to napkins! So, when a square napkin with 9-inch sides is folded along the diagonal, we end up with a right-angled triangle. Using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the two legs of the triangle and c is the hypotenuse (diagonal in this case), we can solve for the diagonal. Since the sides of the square napkin are equal, both legs of the triangle will also be 9 inches. So, the calculation goes like this:
9^2 + 9^2 = c^2
81 + 81 = c^2
162 = c^2
√162 ≈ 12.73
So, the length of the diagonal when the napkin is folded is approximately 12.73 inches. Just don't let that diagonal unfold and trip you up!
To find the length of the diagonal of the square napkin, we can use the Pythagorean theorem.
The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, when the square napkin is folded along the diagonal, it forms a right triangle. The two sides of the square napkin become the legs of the triangle, and the diagonal of the napkin becomes the hypotenuse.
Since the sides of the square napkin are 9 inches long, both legs of the right triangle have a length of 9 inches. Let's call the length of the diagonal "d".
According to the Pythagorean theorem:
d^2 = 9^2 + 9^2
d^2 = 81 + 81
d^2 = 162
To find the length of the diagonal, we need to take the square root of both sides:
d = √162
Using a calculator, we find that the square root of 162 is approximately 12.73.
Therefore, the length of the diagonal of the folded square napkin is approximately 12.73 inches.
To find the length of the diagonal when the napkin is folded along the diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the napkin folded along the diagonal forms a right triangle. The sides of the square napkin act as the legs of the right triangle, and the folded diagonal acts as the hypotenuse.
Given that the sides of the square napkin are 9 inches long, let's call them "a" and "b". The length of the diagonal (hypotenuse) can be represented by "c".
Using the Pythagorean theorem, we have the formula:
c^2 = a^2 + b^2
Since the sides of the square napkin are equal in length (9 inches), we can simplify the equation:
c^2 = 9^2 + 9^2
Simplifying further:
c^2 = 81 + 81
c^2 = 162
To find the length of the diagonal, we need to calculate the square root of 162:
c = √162
c ≈ 12.73 inches
Therefore, when the napkin is folded along the diagonal, the length of the diagonal is approximately 12.73 inches.