To determine the length of the diagonal of a rectangle when the length and breadth are provided, we can use the Pythagorean theorem. This theorem relates the sides of a right-angled triangle, stating that the square of the hypotenuse (the longest side, which would be the diagonal in this case) is equal to the sum of the squares of the other two sides (the length and breadth of the rectangle).
Let's break down the steps to find the length of the diagonal:
1. Identify the given values:
- Length [tex]\( l = 10 \)[/tex] cm
- Breadth [tex]\( b = 20 \)[/tex] cm
2. Apply the Pythagorean theorem:
According to the theorem:
[tex]\[
d^2 = l^2 + b^2
\][/tex]
where [tex]\( d \)[/tex] is the diagonal, [tex]\( l \)[/tex] is the length, and [tex]\( b \)[/tex] is the breadth.
3. Calculate the squares of the length and breadth:
[tex]\[
l^2 = 10^2 = 100
\][/tex]
[tex]\[
b^2 = 20^2 = 400
\][/tex]
4. Add the squares of the length and breadth:
[tex]\[
d^2 = 100 + 400 = 500
\][/tex]
5. Find the square root of the sum to obtain the diagonal:
[tex]\[
d = \sqrt{500} \approx 22.36
\][/tex]
Thus, the length of the diagonal of the rectangle is approximately [tex]\( 22.36 \)[/tex] cm.
