Question

A triangular banner is to be made according to the specifications in the figure shown, with dimensions given in inches.Wooden sticks will be used tq outline the perimeter of the banner in order to attach the interior material.How many inches of wooden sticks will be required?

Answer 1

From the question given, to get how many inches of wooden stick that would be required to outline the perimeter of the banner, we have to find the perimeter of the triangle as shown below

So from above, perimeter is distance around a plane figure. So the perimeter of the triangle will be

`\begin{gathered} 13+15+x+5 \\ 13+15+5+x \\ =33+x \end{gathered}`

so, we need to find the value of x to get the perimeter

From the diagram above you can see that the triangle is made up of two right-triangles. For the smaller right angle triangle, the the hypotenuse is 13, so from Pythagoras, we have

`\begin{gathered} 13^2=5^2+h^2 \\ 169=25+h^2 \\ h^2=169-25 \\ h^2=144 \\ h=√(144) \\ h=12 \end{gathered}`

Now, h is for both the smaller and bigger right angle triangles. So for the bigger triangle, 15 is the hypotenuse. From Pythagoras, we have

`\begin{gathered} 15^2=x^2+h^2 \\ 15^2=x^2+12^2 \\ 225=x^2+144 \\ x^2=225-144 \\ x^2=81 \\ x=√(81) \\ x=9 \end{gathered}`

So, the perimeter becomes

`\begin{gathered} =33+x \\ =33+9 \\ =42 \end{gathered}`

Hence the answer is 42 inches