The diagonal of a rectangle can be measured using the Pythagorean theorem.
Here's a breakdown of how to do it:
Understanding the Concept
The diagonal of a rectangle divides it into two right-angled triangles. The diagonal acts as the hypotenuse of these triangles, while the length and width of the rectangle are the other two sides (legs) of the triangle. The Pythagorean theorem states: a² + b² = c², where 'a' and 'b' are the lengths of the two shorter sides of a right triangle, and 'c' is the length of the hypotenuse.
Applying the Pythagorean Theorem
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Identify the Length and Width: Determine the length (l) and width (w) of the rectangle. These are the 'a' and 'b' in the Pythagorean theorem.
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Apply the Formula: The formula to find the diagonal (d) is: d = √(l² + w²)
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Calculate:
- Square the length (l²).
- Square the width (w²).
- Add the squared values (l² + w²).
- Take the square root of the sum. The result is the length of the diagonal.
Example
Let's say you have a rectangle with a length of 4 units and a width of 3 units.
- l = 4
- w = 3
- d = √(4² + 3²)
- d = √(16 + 9)
- d = √25
- d = 5
Therefore, the diagonal of the rectangle is 5 units.
Summary
To measure the diagonal of a rectangle, use the Pythagorean theorem: d = √(l² + w²), where 'd' is the diagonal, 'l' is the length, and 'w' is the width of the rectangle.
