Question

Can someone please help me I have to turn this in before 11:59pm

Answer 1

`x = (147)/(13)`

Explanation:

Please refer to attached for labeling of the diagram:

We have 2 triangles here in the figure:

`\triangle ABC \text{ and }\triangle BDE`.

1.
`\angle B` is common to both the triangles.

Sides AC || DE (parallel sides):

So, Corresponding angles will be equal

2.
`\angle A = \angle D`

3.
`\angle E = \angle C`

So,
`\triangle ABC \text{ and }\triangle BDE` are similar to each other.

Similar triangles have ratio of their sides as equal.

So,
`AB : BD = BC : BE`

`\Rightarrow (6+7)/(6) = (21)/(21-x)\\\Rightarrow (13)/(6) = (21)/(21-x)\\\Rightarrow 13 * (21-x) = 21 * 6\\\Rightarrow 13x = 7 * 21\\\Rightarrow x = (147)/(13)`

Hence,
`x = (147)/(13)`