1 Answer

David Kuhta · Answer 1 · 2023-05-20T18:44:35+0000

~Given:

The right triangle ABC,

Use the Pythagorean theorem to find the length of the third side

$\begin{gathered} AC=\sqrt[]{20^2+21^2} \\ AC=\sqrt[]{841} \\ AC=29 \end{gathered}$

The triangle DEF IS,

Use Pythagorean theorem.

$\begin{gathered} DF^2=DE^2+EF^2 \\ 58^2=40^2+EF^2 \\ EF^2=1764 \\ EF=42 \end{gathered}$

It is also observed that sides of the triangles DEF are multiple sides of triangle ABC,

$\begin{gathered} DE=40=2* AB \\ EF=42=2* BC \\ DF=58=2* AC \end{gathered}$

Therefore,

$\Delta ABC\text{ \textasciitilde }\Delta DEF$

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