The diagonal of a rectangle or triangle is the line segment connecting the two opposite vertices. It is often called the "diameter" of the shape. The length of...
The diagonal of a rectangle or triangle is the line segment connecting the two opposite vertices. It is often called the "diameter" of the shape.
The length of the diagonal can be found using the Pythagorean theorem, which states that in any right triangle with sides a, b, and c, the square length of the diagonal c^2 = a^2 + b^2.
For instance, in a rectangle with sides a = 5 cm and b = 12 cm, the length of the diagonal can be calculated as c = √5^2 + 12^2 = √25 + 144 = 15√4.
Similarly, in a triangle with sides a = 8 cm and b = 15 cm, the length of the diagonal can be calculated as c = √8^2 + 15^2 = √64 + 225 = 25√5.
The diagonal can also be found using the following steps:
Draw a line segment from one vertex to the other.
Label the lengths of the two sides as a and b.
Use the Pythagorean theorem to calculate the length of the diagonal.
Verify your answer by calculating the square root of the sum of the squares of the two sides.
Remember that the diagonal is not always perpendicular to either side, so its length may be different depending on the angles involved