How to find the diagonal of a rectangle?
Understand the Problem
The question is asking for a method to calculate the length of the diagonal of a rectangle using its dimensions (length and width). This is typically approached using the Pythagorean theorem.
Answer
$d = \sqrt{l^2 + w^2}$
Answer for screen readers
The final answer is derived by calculating $d = \sqrt{l^2 + w^2}$
Steps to Solve
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Identify the dimensions of the rectangle
Let the length of the rectangle be $l$ and the width be $w$.
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Set up the Pythagorean theorem
According to the Pythagorean theorem, the diagonal $d$ of the rectangle can be found using the formula: $$ d = \sqrt{l^2 + w^2} $$
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Substitute the values of length and width
Plug the values of $l$ and $w$ into the formula: $$ d = \sqrt{l^2 + w^2} $$ Calculate the squares of $l$ and $w$.
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Solve for the diagonal
Sum the squares of the length and width, then take the square root of that sum to find the length of the diagonal.
The final answer is derived by calculating $d = \sqrt{l^2 + w^2}$
More Information
The formula for finding the diagonal of a rectangle is derived from the Pythagorean theorem, which relates to right-angled triangles.
Tips
A common mistake is forgetting to square the length and width before summing them. Always apply the squares first and then sum them before taking the square root.
