Question
Find the length of a diagonal of a rectangle if the length of the rectangle is 24 cm and its width is 10cm.
22
26
34
36
324
22
26
34
36
324
Answers
GPT-4o mini
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. The diagonal \(d\) can be calculated using the formula:
\[
d = \sqrt{l^2 + w^2}
\]
where \(l\) is the length and \(w\) is the width of the rectangle.
Given:
- Length \(l = 24 \, \text{cm}\)
- Width \(w = 10 \, \text{cm}\)
Now, we can substitute these values into the formula:
\[
d = \sqrt{(24 \, \text{cm})^2 + (10 \, \text{cm})^2}
\]
Calculating the squares:
\[
d = \sqrt{576 \, \text{cm}^2 + 100 \, \text{cm}^2}
\]
\[
d = \sqrt{676 \, \text{cm}^2}
\]
Now, take the square root:
\[
d = 26 \, \text{cm}
\]
Thus, the length of the diagonal of the rectangle is **26 cm**.
\[
d = \sqrt{l^2 + w^2}
\]
where \(l\) is the length and \(w\) is the width of the rectangle.
Given:
- Length \(l = 24 \, \text{cm}\)
- Width \(w = 10 \, \text{cm}\)
Now, we can substitute these values into the formula:
\[
d = \sqrt{(24 \, \text{cm})^2 + (10 \, \text{cm})^2}
\]
Calculating the squares:
\[
d = \sqrt{576 \, \text{cm}^2 + 100 \, \text{cm}^2}
\]
\[
d = \sqrt{676 \, \text{cm}^2}
\]
Now, take the square root:
\[
d = 26 \, \text{cm}
\]
Thus, the length of the diagonal of the rectangle is **26 cm**.