To find the length of the longest straight line that can be drawn on a rectangular chalkboard with dimensions of 2.2 meters by 1.2 meters, we need to calculate the length of the diagonal of the rectangle. This can be achieved using the Pythagorean theorem.
Here's a step-by-step solution:
1. Understand the Problem:
We need to calculate the length of the diagonal of a rectangle. The diagonal is the longest straight line that can be drawn within the rectangle.
2. Recall the Pythagorean Theorem:
For a right-angled triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. In the context of a rectangle:
[tex]\[
\text{diagonal}^2 = \text{length}^2 + \text{width}^2
\][/tex]
3. Identify the Length and Width:
From the problem, we know the length (L) of the chalkboard is 2.2 meters and the width (W) is 1.2 meters.
4. Apply the Pythagorean Theorem:
[tex]\[
\text{diagonal}^2 = L^2 + W^2
\][/tex]
Substituting the length and width:
[tex]\[
\text{diagonal}^2 = (2.2)^2 + (1.2)^2
\][/tex]
5. Calculate the Squares of the Dimensions:
[tex]\[
(2.2)^2 = 4.84
\][/tex]
[tex]\[
(1.2)^2 = 1.44
\][/tex]
6. Sum These Values:
[tex]\[
\text{diagonal}^2 = 4.84 + 1.44 = 6.28
\][/tex]
7. Find the Square Root to Get the Diagonal:
[tex]\[
\text{diagonal} = \sqrt{6.28} \approx 2.506 \, \text{meters}
\][/tex]
Therefore, the length of the longest straight line that can be drawn on the rectangular chalkboard is approximately 2.506 meters.
