Question

In ABCD BH | AD and BG| CD if ab= 16 bc = 12 and bh= 14, find the length of altitude BG to side CD

Answer 1

There should be a picture to with this question.

Answer 2

The symbols you posted should likely be perpendicular symbols

Answer 3

Ok

Answer 4

Okay give me a minute to take a look at this.

Answer 5

So there are a few things we should understand regarding this particular problem.

1. Opposite sides and angles of parallelograms are congruent.
2. Understanding that, we need to show that \(\triangle ABH \sim \triangle{CBG}\)
3. Once we have shown that, we should be in good position to find what is required.

Answer 6

Okay I understand

Answer 7

Basically, we know the triangles are similar because segments BH and AD are perpendicular. Segments BG and CD are perpendicular. Which means angles H and G are right angles.

Answer 8

Furthermore, angles A and C are congruent. Because of this, we know triangles AHB and CGB are similar.

Answer 9

Therefore, we can use the following proportion to find the length of BG:

\(\dfrac{AB}{BH} = \dfrac{CB}{BG}\)

Answer 10

21/2 ?

Answer 11

Okay so BG = 10.5. But now we need to find the length of segment CD. How might we figure out the length of segment CD?

Answer 12

Cd=16

Answer 13

Very good. So what is the length of the altitude of segment BG to side CD?

Answer 14

10.5

Answer 15

Well, actually it was asking for a fraction. The length of the altitude of segment BG would the numerator and the length of side CD would be the denominator.

Answer 16

21/2

Answer 17

Not correct

Answer 18

Hint: \(\dfrac{BG}{CD}\)

Answer 19

BTW, We know 21/2 = BG. That goes in the numerator:

\(\dfrac{21/2}{CD}\)

You told me the length of \(\overline{CD}\) earlier so I know you know it.

Answer 20

What's the answer 21/32

Answer 21

Correct

Answer 22

Thank you

Answer 23

Welcome