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Diagonals of Rectangle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Diagonals of RectangleDiagonals of Rectangle: Definition and ExamplesTable of ContentsDiagonals of a Rectangle Definition of Diagonals in a Rectangle

A diagonal of a rectangle is a line segment that connects two opposite vertices (corners) of the rectangle. In any rectangle, there are always exactly two diagonals. A rectangle is a four-sided shape (quadrilateral) with opposite sides equal in length and all four angles measuring 909090 degrees. The word "diagonal" comes from Greek "diagonios" meaning "from angle to angle," and these lines play an important role in understanding rectangle properties.

The diagonals of a rectangle have several key properties. First, both diagonals are equal in length (congruent). Each diagonal divides the rectangle into two identical right-angled triangles. When the diagonals intersect, they bisect each other (cut each other in half), though they are not perpendicular to each other like in a square. The diagonals form the hypotenuse of the right triangles created when the rectangle is divided. The length of a diagonal can be found using the formula d=w2+l2d = \sqrt{w^2 + l^2}d=w2+l2​, where ddd is the diagonal length, www is the width, and lll is the length of the rectangle.

Examples of Diagonals in a Rectangle Example 1: Identifying Parts of a Rectangle Problem:

Identify the length, width and diagonal in the given rectangle ABCD.

Diagonals of Rectangle

Step-by-step solution:

Step 1, Look at the rectangle ABCD. We need to find which sides are the length, which are the width, and which lines are the diagonals.

Step 2, The length of the rectangle refers to the longer sides. In rectangle ABCD, the lengths are sides AD and BC.

Step 3, The width of the rectangle refers to the shorter sides. In rectangle ABCD, the widths are sides AB and CD.

Step 4, The diagonals are the lines that connect opposite corners. In rectangle ABCD, the diagonals are AC and BD.

Example 2: Finding the Length of a Diagonal Problem:

Find the length of each diagonal of a rectangle of length 151515 units and width 888 units.

rectangle

Step-by-step solution:

Step 1, Write down what we know. The length of the rectangle is 151515 units and the width is 888 units.

Step 2, Recall the formula for finding the diagonal of a rectangle: d=w2+l2d = \sqrt{w^2 + l^2}d=w2+l2​, where ddd is the diagonal, www is the width, and lll is the length.

Step 3, Plug in the values we know into the formula: d=82+152d = \sqrt{8^2 + 15^2}d=82+152​

Step 4, Calculate the squares: d=64+225d = \sqrt{64 + 225}d=64+225​

Step 5, Add the values inside the square root: d=289d = \sqrt{289}d=289​

Step 6, Find the square root: d=17d = 17d=17 units

Step 7, State the answer: The length of each diagonal is 171717 units.

Example 3: Finding the Length of a Rectangle Using the Diagonal Problem:

Find the length of the rectangle if the width of the rectangle is 333 inches, and the diagonal of the rectangle is 555 inches.

rectangle

Step-by-step solution:

Step 1, Write down what we know. The width of the rectangle is 333 inches and the diagonal is 555 inches. We need to find the length.

Step 2, Recall that we can use the Pythagorean theorem since the diagonal forms a right triangle with the sides of the rectangle:

(Diagonal)2=(Length)2+(Width)2(Diagonal)^2 = (Length)^2 + (Width)^2(Diagonal)2=(Length)2+(Width)2

Step 3, Substitute the known values into the equation:

52=l2+325^2 = l^2 + 3^252=l2+32

Step 4, Simplify the squared values:

25=l2+925 = l^2 + 925=l2+9

Step 5, Solve for l2l^2l2 by subtracting 999 from both sides:

l2=25−9=16l^2 = 25 - 9 = 16l2=25−9=16

Step 6, Take the square root of both sides to find the length:

l=16=4l = \sqrt{16} = 4l=16​=4 inches

Step 7, State the answer: The length of the rectangle is 444 inches.

Comments(2)EEntrepreneurKimNovember 4, 2025I've used this glossary page to teach diagonals of rectangles. The clear def and examples really helped my students grasp the concept!

MCMs. CarterSeptember 17, 2025I used the 'Diagonals of Rectangle' page to help my kids with their homework, and it made things so much clearer! The step-by-step examples were super helpful. Great resource for visual learners!

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