Is the diagonal of a rectangle the same as the width of the rectangle?

Answer 1

No it is not.

Answer 2

No. Think of a regular rectangle. Drawing in a diagonal (a line connecting the top right corner to the bottom left corner, or the top left corner to the bottom right corner) will effectively create 2 right triangles. The diagonal is the hypotenuse for both triangles. The length and width of the rectangle serve as the legs for the triangle. You can use the Pythagorean Thoerem to determine that the hypoteneuse (diagonal) will be the longest side: The sum of the squares of the 2 legs equals the square of the hypoteneuse.

Answer 3

No, the diagonal is always longer than the width.

As per Pythagoras theorem, in any right angled triangle, the square of the hypothenuse is equal to sum of the square of its other two sides in a triangle.

If you draw a diagonal in a rectangle, you get two right angled triangles. Let us assume the width of a rectangle is 4 inches and its height (or i.e. other side ) is 3 inches. Then we calculate the length of the diagonal as follows:

Square of diagonal length (i.e. hypothenuse) = 3 square + 4 square
or that is
Square of diagonal length = 9 + 16 = 25
Hence hypothenuse = square root of 25 = 5 inches

So you see, the diagonal length is always more than the width in any rectangle.

Answer 4

In any rectangle or square the length of the diagonal is never the same lenght as the width or the length of that square or rectangle. Here's some simple geometry to prove this:

If you have a square or rectangle with a length (we'll call this measurement A) and a width (we'll call this measurement B), then you draw a line from one corner to the other creating two triangles (we'll call this measurement C). Then you can create a formula to determine the lenght of any side of that triangle if you know the other two lenghts. This formula is as stated A2+B2=C2. The two meaning squared, I don't know how to type squared sorry.

So if you have a rectangle with a length (measurement A) of 5 inches and a width of 4 inches (measurement B), we can find the exact length of the diagnal (measurement C) by punching in the numbers into our formula.

(5)2+(4)2=C2
(5x5)+(4x4)=C2
25+16=C2
41=C2
Then you must do some algebra.
To get just C you must square root both sides of the equation
C=6.40 inches

Hope this helps in your math.

Answer 5

No. First imagine the rectangle as a piece of paper, one side is 8.5 (a) inches and the other side is 11(b) inches. The width of this rectangle would be 8.5(a) inches. To calculate the diagonal you would need to use The Pythagorean Theorem.
(that is a^2 + b^2 = c^2, where a = 8.5, b = 11, and c = diagonal)
So (8.5 squared) + (11 squared) = (c squared)
this give 72.25 + 121 = c^2, or 193.25 = c^2
So to find c take the square root of 193.25 which = 13.90
Therefore 13.90 is the legnth of the diagonal (in this case) that bisects the rectangle. (i.e. splits the reactangle into two equal triangles.)

Answer 6

No the diagonal is longer. The diagonal of a rectangle is equal to the height squared + the width ( or length) squared; (a squared + b squared = c squared) When you draw a diagonal in a rectangle you have created two triangles.

Answer 7

No. The width of the rectangle is the distance between the two corners that are adjacent to one another horizontally. The diagonal is the distance between two opposing corners.

Answer 8

Assuming the rectangle is 4 90 degree corners the diagonal is not equal to the width.

a = height
b = width
c = diagonal (hypotenuse)

a^2 + b^2 = c^2

That's how you can figure it out.

Answer 9

No, to find the length of the diagonal use the pythagorean theorem. In this case the diagonal is the square root of (length squared + width squared)

Answer 10

No, it's much longer. You can figure out it's length using the pythagorean theorem: side 1^2+side 2^2=side 3^2, with side 3 as the diagonal.

Answer 11

No...the diagonal is not...it's length is the square root of the sum of the sides squared. The width is the same as the length of the top edge (or bottom edge).