Question

Find the length of a diagonal of a rectangle if the length of the rectangle is 24 cm and its width is 10 cm.
Responses
A 22 cm22 cm
B 26 cm26 cm
C 34 cm34 cm
D 36 cm36 cm
E 324 cm

Answer 1

To find the length of the diagonal of a rectangle, you can use the Pythagorean theorem. The formula for the diagonal \(d\) of a rectangle is given by:

\[
d = \sqrt{L^2 + W^2}
\]

where \(L\) is the length and \(W\) is the width of the rectangle.

Given:
- Length \(L = 24 \text{ cm}\)
- Width \(W = 10 \text{ cm}\)

Plugging the values into the formula:

\[
d = \sqrt{(24)^2 + (10)^2}
\]

Calculating each square:

\[
(24)^2 = 576
\]
\[
(10)^2 = 100
\]

Now, adding these two:

\[
576 + 100 = 676
\]

Now, take the square root:

\[
d = \sqrt{676} = 26 \text{ cm}
\]

Therefore, the length of the diagonal of the rectangle is **26 cm**.

The correct response is **B** (26 cm).