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Q: What is the side length of a square with a diagonal of 16?

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A "regular quadrilateral" is a square. The word "radius" isn't used for squares (or polygons in general). To get the length of a side, divide the perimeter by 4. To get the diagonal of a square, multiply the length of a side by the square root of 2.

10' x 16' is not a square but a rectangle and the diagonal is square root of (10^2 + 16^2) = square root of (100 + 256) = square root of 356 which is 18.867 feet

A side length would be 64/4 which is 16 16 times 16 is 256

A square can't have a side of 16 m2 (square meters). That's a unit of area, not a unit of length. A length can be in meters, centimeters, etc. Once you have the correct measure for the side, just multiply it by itself to get the area.

The perimeter of a plane figure is the length of its boundary. Thus the perimeter of a square of length L is 4L. So the perimeter of a square of length 4 is 4 x 4 = 16 (4 + 4 + 4 + 4 = 16). The perimeter of a circle is the length of its circumference.If you are asking for the circumference of the circle circumscribed and inscribed in this square, their circumference will be:First, we need to find the measure length of their radius. We know that the diagonals of the square form 4 congruent isosceles triangles with the base length equal to the length of the square, and length side equal one half of the diagonal length ( the diagonals of a square are equal in length and bisect each other (and bisect also the angle of the square ), so the center of the circumscribed circle of the square will be the point of their intersection, and its radius will be the one half of the diagonal of the square). We can find the diagonal length by using the Pythagorean theorem. So from the right trianglewhich is formed by drawing one of the diagonals, we find the length of the diagonal which is also the hypotenuse of this right triangle, and which is equal to square root of[2(4^2)]. So the length of the diagonal is equal 4(square root of 2), and its half is 2(square root of 2), which is the length of the radius of the circumscribed circle. So its circumference is equal to (2)(pi)(2(square root of 2)) = 4(square root of 2)pi.Now, we need to know what is the length of the radius of the inscribed circle, and what is this radius. Let's look at the one of the fourth triangles that are formed by drawing the two diagonals of the square. If we draw the perpendicular from the intersection of the diagonals to the side of the square, this perpendicular is the median of the side of the square and also the altitude of this isosceles triangle. Let's find the measure of its length. Again we can use the Pythagorean theorem. So this measure is equal to the square root of [(2(square root of 2))^2] - 2^2] which is equal to 2. If we extend this perpendicular to the side of the triangle and draw another perpendicular from the point of the intersection of the diagonals to the other sides of the square, their length will be also 2. Since they have the same distance from the point of the intersection of the diagonals, we can say that their length is the length of the radius of the inscribed circle, and the point of the intersection of the diagonals is also its center. So the measure of length of the radius is 2, and the circumference of the inscribed circle is (2)(pi)(r) = (2)(pi)(2) = 4pi.As a result, we can say that the point of the intersection of the diagonals of a square is the center of its inscribed and circumscribed circle, and the perpendicular lines drawing from this point to the sides of the square bisect each other. (These perpendiculars are parallel and equal in length to the square length, because we know that two lines that are perpendicular respectively to the other two parallel lines, are equal in length and parallel between them). We also can say that in an isosceles triangle with 45 degrees base angle, the median is not only also an altitude, but its length is one half of the length of the base.

Related questions

The length of one side of a square with a 16-centimeter diagonal is: 11.31 cm

It is 16*sqrt(2) feet.

Using Pythagoras' theorem the diagonal is 16 times the square root of 2

A "regular quadrilateral" is a square. The word "radius" isn't used for squares (or polygons in general). To get the length of a side, divide the perimeter by 4. To get the diagonal of a square, multiply the length of a side by the square root of 2.

16*sqrt(2) = 22.627 (to 3 dp).

Designate the length by L. From the Pythagorean theorem, the length of the diagonal of a square, which divides the square into two right triangles, each with sides L (and the diagonal as hypotenuse to each right triangle), is square root of 2L2 = 4 (from the problem statement). Squaring both sides separately yields 2L2 = 16 or L = square root of 8 = 2 (square root of 2).

If the perimeter is 64, then one side is 16. The diagonal is the hypotenuse of a right triangle. Hello Pythagoras. The answer is the square root of 512 or 16 times the square root of 2.

5.7 ft

A square with a side length of 16 inches has an area of 256 square inches.

The diagonal of a rectangle is the third and longest side of a triangle with sides the same as those of the rectangle, so its length is the square root of the sum of the squares of the lengths of the sides of the triangle, (Pythoagoras' Theorem) which are also the sides of the rectangle. If the rectangle is 3 inches by 4 inches, then the diagonal is the square root of 3 squared (= 9) and 4 squared (= 16) so the diagonal is the square root of 16 + 9 = 25, giving it the length of 5 inches.

If you take the square of the long side and add it to the square of the short side, you get the diagonal (hypotenuse) squared. Then just find square root of that. For example, if short side is 3cm and long side is 4cm: 9 + 16 = 25, so the diagonal would be the square root of 25 ie. 5.

Each side is 4. The diagonal is 5.66 and the area is 16 square units.

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