Question

The width of a rectangle is 7 centimeters, and the length of the rectangle is 8 centimeters. Which measurement is closest to the diagonal of this rectangle in centimeters?
Responses

A 113 cm113 cm

B 12.5 cm12.5 cm

C 122 cm122 cm

D 10.6 cm

Answer 1

To find the diagonal of a rectangle, you can use the Pythagorean theorem. The formula for the diagonal \( d \) of a rectangle with width \( w \) and length \( l \) is:

\[
d = \sqrt{w^2 + l^2}
\]

Given:
- Width (\( w \)) = 7 cm
- Length (\( l \)) = 8 cm

Now, plug in the values:

\[
d = \sqrt{7^2 + 8^2} = \sqrt{49 + 64} = \sqrt{113}
\]

Calculating \( \sqrt{113} \):

\[
\sqrt{113} \approx 10.63014581 \ldots
\]

So, the diagonal is approximately 10.63 cm.

The closest measurement to this value from the options provided is:

D) 10.6 cm.