Question

What is the length of the dotted line in the diagram below? Round to the nearesttenth.

Answer 1

From the given figure

The rectangle has a width of 3 and its length is the hypotenuse of a right triangle with legs 5 and 7

Then we will find at first the hypotenuse of the triangle using the Pythagoras Theorem

`\begin{gathered} L=\sqrt[]{7^2+5^2} \\ L=\sqrt[]{49+25} \\ L=\sqrt[]{74} \end{gathered}`

Now, to find the dotted line we will do the same with the length and the width of the rectangle

`\begin{gathered} D=\sqrt[]{L^2+W^2} \\ L=\sqrt[]{74},W=3 \\ D=\sqrt[]{(\sqrt[]{74})^2+(3)^2} \\ D=\sqrt[]{74+9} \\ D=\sqrt[]{83} \\ D=9.110433579 \end{gathered}`

Round it to the nearest tenth

The length of the dotted line is 9.1