Question

Determine x. (Figure not drawn to scale.)

Answer 1

What do you know about the two triangles?

Answer 2

I thought it was considered as one..

Answer 3

There are two triangles, BCD and ACE.
The triangles are not congruent since they are different sizes.
What are the triangles?

Answer 4

What do you mean? What type?

Answer 5

The triangles are not congruent, but their shapes are the same, only the sizes are different. What are they?

Answer 6

Scalene

Answer 7

They may be scalene, but what I am trying to arrive at is "similar."
If the angles of one triangle are congruent to the corresponding angles of another triangle, then the triangles are similar.
Similar triangles have lengths of sides that are proportional.

In this case, you have triangle CBD and triangle CAE.

Angle C of triangle CBD is congruent to angle C of triangle CAE since it's the same angle.
Angle CBD of triangle CBD is congruent to angle CAE of triangle CAE because they are corresponding angles of parallel lines.
Angle CDB of triangle CBD is congruent to angle CEA of triangle CAE because they are corresponding angles of parallel lines.

Since all three angles of triangle CBD are congruent to the corresponding angles of triangle CAE, triangles CBD and CAE are similar. Their lengths sides are proportional.
To be proportional means the ratios are equal.

Side CD of triangle CBD corresponds to side CE of triangle CAE.
The ratio of the lengths is:

\(\dfrac{CD}{CE} = \dfrac{1.4}{1.4 + 2.5} = \dfrac{1.4}{3.9} \)

Side BD of triangle CBD corresponds to side AE of triangle CAE.
The ratio of the lengths is:

\(\dfrac{BD}{AE} = \dfrac{x}{x+3.5} \)

Since the lengths of the sides, the ratios of the lengths are equal:

\(\dfrac{1.4}{3.9} = \dfrac{x}{x+3.5} \)

Now you need to solve the equation above for x.

Answer 8

Is cross multiplication done to find x?

Answer 9

3.9x=1.4(x+3.5)

3.9x= 1.4x+4.9

2.5x=4.9

x= 1.96

Is this correct?

Answer 10

Cross multiplication is good.
Yes, x = 1.96 is correct.