Question

Find x.

Answer 1

@mathmate

Answer 2

@Hero @jigglypuff314

Answer 3

Those 2 triangles are not congruent for sure so since they asked for x they should be either congruent or similar. and since the base sides aren't identical then the triangles are not congruent they are actually similar

Answer 4

Any ideas about how to solve? and what did you get so far

Answer 5

That isn't quite correct. because 2 in the 1st triangle should be the measure of the base

Answer 6

oh ok so

Answer 7

There are three rules for this kind of problem:

Referring to the figure above, which contains two right angles, or contains an altitude dropped from the right-angle of a triangle.
Note that c is the length of the hypotenuse, so c=p+q
Try an example where
a=3, b=4, c=5, p=1.8, q=3.2, h=2.4

a^2+b^2=c^2 .........(Pythagoras) [3^2+4^2=5^2, ok]
a*b=c*h ................(just two different ways of calculating twice the area of triangle)
[3*4=2.4*5=12 ok]
a^2=p*c ...............[ 3^2=1.8*5=9, ok]
b^2=q*c................ [4^2=3.2*5=16, ok]
and finally
h^2=pq ...............[2.4^2=1.8*3.2=5.76, ok]

These are metric relations which are very useful in solving geometric problems with an altitude from the right-angle of a triangle.

Answer 8

how did you find the measure of side h in your pic? @mathmate because the whole question depend on finding that side

Answer 9

The question depend on the metric relation
a^2=p*c

All the metric relations repose on the three similar triangles, and can be proved using similar triangles.
For your information, h can be found using relationship h^2=pq.

Answer 10

ok this stuff is waaaay over my head... is there a more simple way to solve this?

Answer 11

that's good to know. :) but shes taking Geometry B that is an advanced level that you solving in

Answer 12

@Will.H haha thanks yeah i didn't understand like any of that XD

Answer 13

However good luck with whatever you do. And BTW you can solve that using the trigonometric functions

Answer 14

@Will.H
OP should have learned in class the following, which is a summary, and presented with pretty illustrations:
http://marceau.pbworks.com/w/file/fetch/53043928/MetricRelationsRightTriangle.pdf

Answer 15

thats a very useful website, thank you. My point is. you need to solve any problem using the level that he/she taking.

Answer 16

sooo can anyone actually tell me how to solve it?? haha

Answer 17

tell me what module are you at, and what is the name of the module, i can solve this by ratio and similar triangles or by trigonometric functions. or you can follow the steps that @mathmate mentioned

Answer 18

module??

Answer 19

like what unit, you taking online classes aren't you!

Answer 20

yes im in geometry b like you said

Answer 21

im on similar polygons

Answer 22

i know. but which unit what is the name of the lesson that this question is in

Answer 23

okay

Answer 24

triangles and trigonometry is the nameof the lesson

Answer 25

@will_h
Metric relations were taught at grade 10 (i.e. 10th year from elementary).
It is possible to derive every one of the relations using similar triangles, for example,
for deriving
a^2=p(p+q) , OP can show instead the following using basic similar triangles
1. prove BAC~DBA
2. prove DBA~DAC
3. conclude
\(\Large \frac{p}{a}=\frac{h}{b}=\frac{a}{p+q}\)
4. hence conclude
\(\Large \frac{p}{a}=\frac{a}{p+q}\)
or
\(a^2=p(p+q)\)=p*c

Answer 26

i really agree with i never said i don't

Answer 27

let me make that simple for her

Answer 28

@Will.H
Excellent!

Answer 29

These are the triangles we haave