Question

A DJ is creating a geometrical stage setup. All his equipmentwill be on a triangular shaped platform. If two sides of theplatform measure 4 feet and 9 feet, which of the followingcould be the length of the third side? Select all that apply.a. 3 feetb. 4 feetc. 7 feetd. 12 feete. 14 feetf. 15 feetg. 10 feet

Answer 1

We are gonna apply the Pythagorean theorem

h = 9

a = 4

`\begin{gathered} h^2=a^2+b^2 \\ b=\sqrt[]{h^2-a^2} \\ b=\sqrt[]{9^2-4^2} \\ b=\sqrt[]{81-16} \\ b=\sqrt[]{65} \\ b=8.062 \end{gathered}`

Now we are gonna calculate all the values

`\begin{gathered} a+b>c \\ 9+4>c \\ 13>c \end{gathered}`

Triangle Inequality |4-9|

[tex]\begin{gathered} |-5|The answers would be

c. 7 feet

d. 12 feet