Question

5. A small rectangular tray measures 16 cm by 18 cm. Determine the length of the diagonal. Round your answer to the nearest tenth. A 16 cm B 256 cm C 24.1 cm D 26.3 cm

Answer 1

24.1 cm

Step-by-step explanation

First, let us make a sketch of the question:

We see that the diagonal and the sides of the rectangle form two equal right angled triangles.

To find the length of diagonal, we have to apply Pythagoras Rule:

`\text{hyp}^2=a^2+b^2`

where hyp = hypotenuse = D

a and b = legs of the triangles (16 cm and 18 cm)

So, we have that:

`\begin{gathered} D^2=16^2+18^2 \\ D^2\text{ = 256 + 324} \\ D^2\text{ = 580} \\ Find\text{ the square root of both sides:} \\ D\text{ = }\sqrt[]{580} \\ D\text{ }\cong24.1\text{ cm} \end{gathered}`

The length of the diagonal is 24.1 cm.