A square tablecloth has a line of embroidered flowers along the diagonal. The tablecloth is 48 inches on each side. How long is the embroidery line? Round to the nearest inch.
48 * sqrt2 .
Do the numbers
would it be 6.92 then when you round it would be 7 inches right??
To determine the length of the embroidery line, we need to find the length of the diagonal of the square tablecloth.
Using the Pythagorean theorem, we can calculate the length of the diagonal.
The Pythagorean theorem states that in a right triangle, the square 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 two sides of the right triangle are the sides of the square tablecloth.
Let's call the length of each side of the square tablecloth "a" inches.
Using the Pythagorean theorem, we have:
a^2 + a^2 = diagonal^2
2a^2 = diagonal^2
diagonal^2 = 2a^2
Taking the square root of both sides, we have:
diagonal = sqrt(2a^2)
diagonal = sqrt(2 * 48^2)
diagonal = sqrt(2 * 2304)
diagonal ≈ sqrt(4608)
diagonal ≈ 67.82 inches
Therefore, the length of the embroidery line is approximately 67.82 inches, rounded to the nearest inch.
To find the length of the embroidery line, we need to determine the length of the diagonal of the square tablecloth.
We know that a square has four equal sides, so each side of the tablecloth measures 48 inches. Since the tablecloth is a square, all four sides are the same length.
To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right triangle are the sides of the tablecloth, and the hypotenuse is the diagonal.
Let's consider one side of the tablecloth as a leg of the right triangle, and the diagonal as the hypotenuse. The length of one side is 48 inches.
Using the Pythagorean theorem, we can calculate the length of the diagonal (d) as follows:
d^2 = (48 inches)^2 + (48 inches)^2
d^2 = 2304 square inches + 2304 square inches
d^2 = 4608 square inches
To find the value of d, we need to take the square root of both sides:
d = √(4608 square inches)
Using a calculator, we find that the square root of 4608 is approximately 67.882 inches.
Since we are asked to round to the nearest inch, the length of the embroidery line on the diagonal of the tablecloth is approximately 68 inches.