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

What Is The Length Of The Dotted Line In The Diagram Below Round To The Nearesttenth class=

Sagot :

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

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

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

[tex]\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}[/tex]

Round it to the nearest tenth

The length of the dotted line is 9.1

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