Question

The side lengths of a triangle are shownbelow. How many other triangles with thesemeasurements could be made?A. None just this unique triangleB. Two trianglesC. Many triangles84 mm96 mm60 mm

Answer 1

Given the side lengths of some triangle:

`\begin{gathered} L_1=84 \\ L_2=96 \\ L_3=60 \end{gathered}`

Let us suppose that there exists another triangle with these side lengths:

`\begin{gathered} L_1^(\prime)=84 \\ L_2^(\prime)=96 \\ L_3^(\prime)=60 \end{gathered}`

Based on these, we can say that:

`\begin{gathered} L_1\cong L_1^(\prime) \\ L_2\cong L^(\prime)_2 \\ L_3\cong L^(\prime)_3 \end{gathered}`

Then, using the Side-side-side theorem, we conclude that both triangles are congruent, so this triangle is unique