Question

2 triangles are shown. The first triangle has side lengths x, x, 50. The second triangle has side lengths 45, 45, 75.What value of x will make the triangles similar by the SSS similarity theorem?

Answer 1

Two triangles are similar if their corresponding sides have an equal ratio

Since the sides of the 1st triangle are x, x, and 50

Since the sides of the 2nd triangle are 45, 45, and 75

Since the two triangles are similar by the SSS theorem, then

`(x)/(45)=(x)/(45)=(50)/(75)`

By using the cross-multiplication between the 1st or 2nd ratio and the 3rd ratio

`\begin{gathered} (x)/(45)=(50)/(75) \\ x*75=45*50 \\ 75x=2250 \end{gathered}`

Divide both sides by 75

`\begin{gathered} (75x)/(75)=(2250)/(75) \\ x=30 \end{gathered}`

The value of x is 30