Question

Use the picture shown to solve for inequalities in two triangles

Answer 1

GIVEN

Two triangles ABC and ACD where two corresponding sides of the two triangles are equal.

SOLUTION

The two triangles have equal sides such that:

`\begin{gathered} AB=AD \\ and \\ AC=AC \end{gathered}`

By this, the length of the remaining sides BC and DC are related such that the side opposite the greater angle has the greater length.

Since
`BC>DC`Substitute known values into the inequality:

`\begin{gathered} DC=11x-33 \\ BC=77 \\ \therefore \\ 77>11x-33 \end{gathered}`

Solving the inequality:

`\:x<10`

Recall that the side DC has to be greater than 0. Therefore:

`\begin{gathered} 11x-33>0 \\ \therefore \\ x>3 \end{gathered}`

Combining both solutions:

[tex]3ANSWER