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