To solve the problem and measure the length of the diagonal of a rectangle with the given dimensions, we need to follow the geometric properties of the rectangle. Here's the step-by-step solution:
1. Understanding the problem:
We have a rectangle with the dimensions of 7.4 cm in length and 10.3 cm in width. We need to measure the diagonal of this rectangle.
2. Recalling the properties of a rectangle:
A rectangle has right angles (90°) at each corner. The diagonal of a rectangle divides it into two right-angled triangles, and within each triangle, we can apply the Pythagorean theorem.
3. Using the Pythagorean theorem:
The Pythagorean theorem states:
[tex]\[
c^2 = a^2 + b^2
\][/tex]
where [tex]\(c\)[/tex] is the hypotenuse (diagonal in this case), and [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are the other two sides (length and width of the rectangle).
4. Assigning values:
In our case:
[tex]\[
a = 7.4 \text{ cm}
\][/tex]
[tex]\[
b = 10.3 \text{ cm}
\][/tex]
5. Calculating the diagonal:
Substituting the values into the Pythagorean theorem:
[tex]\[
c = \sqrt{(7.4)^2 + (10.3)^2}
\][/tex]
6. Finding the numerical result:
The calculated length of the diagonal is:
[tex]\[
c \approx 12.68266533501535 \text{ cm}
\][/tex]
So, the length of the diagonal of the rectangle measuring 7.4 cm by 10.3 cm is approximately 12.68 cm.
