Question

Jannette says because 's sides form a Pythagorean triple and 's side lengths are multiples of 's side lengths. Is she correct? Explain your reasoning.

Answer 1

The similar triangles ABC and DEF may or may not have equal lengths

Janette's claim that triangles ABC and DEF are similar triangle is true

How to prove or disprove Janette's claim?

Start by calculating the length of the third sides using the Pythagoras theorem.

$a^2 = b^c + c^2$

For triangle ABC, we have:

$AC^2 = 20^2 + 21^2$

$AC = 29$

For triangle DEF, we have:

$58^2 = 40^2 + EF^2$

This gives

$EF^2 = 58^2 - 40^2$

$EF = 42$

So, we have the following corresponding lengths on both triangles

Triangle ABC             Triangle DEF               Common ratio

20                                      40                                    2

21                                       42                                    2

29                                      58                                    2

Since the common ratios are the same, then the triangles are similar

Hence, Janette's claim is true

Read more about similar triangles at:

https://brainly.com/question/14285697