How to calculate the diagonal length of a rectangle?
Understand the Problem
The question is asking for the method to compute the diagonal length of a rectangle. To find the diagonal, we can use the Pythagorean theorem, which states that the square of the diagonal (d) is equal to the sum of the squares of the length (l) and width (w) of the rectangle: d = √(l² + w²).
Answer
The diagonal length $d$ is approximately $5.83$ units.
Answer for screen readers
The length of the diagonal $d$ is approximately $\sqrt{34}$ or about 5.83 units.
Steps to Solve
- Identify the dimensions of the rectangle
First, gather the length ($l$) and the width ($w$) of the rectangle. These measurements are essential for calculating the diagonal.
- Apply the Pythagorean theorem
Using the Pythagorean theorem, express the formula for the diagonal ($d$) of the rectangle:
$$ d = \sqrt{l^2 + w^2} $$
- Square the dimensions
Calculate the squares of the length and width. For example, if the length is 5 units and the width is 3 units, compute:
$$ l^2 = 5^2 = 25 $$
$$ w^2 = 3^2 = 9 $$
- Sum the squared dimensions
Add the squared values obtained in the previous step:
$$ l^2 + w^2 = 25 + 9 = 34 $$
- Take the square root
Finally, take the square root of the sum from the last step to find the diagonal:
$$ d = \sqrt{34} $$
- Calculate the numerical value
Calculate the numerical value of the diagonal. For $\sqrt{34}$, the approximate value is about 5.83.
The length of the diagonal $d$ is approximately $\sqrt{34}$ or about 5.83 units.
More Information
The diagonal of a rectangle can be visualized as a line connecting opposite corners, and using the Pythagorean theorem helps find its exact length. This concept is widely applicable in various fields, including architecture and design.
Tips
- Confusing length and width values.
- Forgetting to square the dimensions before adding.
- Not taking the square root of the sum to find the diagonal.
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