Question

7. AABC has side lengths 14, 8, and 10.4What are possible side lengths of ADEF ifAABC - ADEF?

Answer 1

Given triangle ABC with side lengths;

`\begin{gathered} AB=14 \\ BC=8 \\ AC=10.4 \end{gathered}`

If triangle ABC is congruent to triangle DEF, then it means;

For the triangles to be congruent, then there must be a similar ratio that exists between all three sides of both triangles. This means, for instance, if one side of triangle ABC is dilated by a factor of 2 to get the length of the corresponding side in triangle DEF, the same factor must apply to the remaining two sides.

Therefore, from the options provided;

`\begin{gathered} \text{Option F} \\ (14)/(28)=(1)/(2),(8)/(20)=(2)/(5),(10.4)/(20.8)=(1)/(2) \\ \text{Not Correct} \end{gathered}`
`\begin{gathered} \text{Option G} \\ (14)/(35)=(2)/(5),(8)/(16)=(1)/(2),(10.4)/(20.8)=(1)/(2) \\ \text{Not correct} \end{gathered}`
`\begin{gathered} Option\text{ H} \\ (14)/(28)=(1)/(2),(8)/(20)=(2)/(5),(10.4)/(26)=(2)/(5) \\ \text{Not correct} \end{gathered}`
`\begin{gathered} Option\text{ J} \\ (14)/(35)=(2)/(5),(8)/(20)=(2)/(5),(10.4)/(26)=(2)/(5) \\ \text{Correct} \end{gathered}`

ANSWER:

Option J is the correct answer.

This is because all the three sides of triangle ABC which are 14, 8 and 10.4 when multiplied by a factor of 5/2 would yield the sides 35, 20 and 26 for the other triangle DEF.

This is not true for the other options F, G and H.