# Thread: length of a line inside a triangle, given all sides

1. ## length of a line inside a triangle, given all sides

what is the length of x? the answer is 9

i can not do it from similar triangles as there is only one similar angle, or can i? all i can think of is similar triangles here

also 7x16=112 and 8 x 14 = 112 and 7x8 = 56. so the solution has to do with this i think.... but what is the relation....

2. ## Re: length of a line inside a triangle, given all sides

Originally Posted by ketanco
what is the length of x? the answer is 9

i can not do it from similar triangles as there is only one similar angle, or can i? all i can think of is similar triangles here

also 7x16=112 and 8 x 14 = 112 and 7x8 = 56. so the solution has to do with this i think.... but what is the relation....
Draw triangle OBE and triangle ABC separately marking the lengths you know.
Angle B is the same in both (I think that's what you mean by one "similar" angle).
Can you now prove the triangles are similar using one of AAA, SSS, SAS etc?

3. ## Re: length of a line inside a triangle, given all sides

Originally Posted by Debsta
Draw triangle OBE and triangle ABC separately marking the lengths you know.
Angle B is the same in both (I think that's what you mean by one "similar" angle).
Can you now prove the triangles are similar using one of AAA, SSS, SAS etc?
yes thats what i meant....
by the way not O, but D.. not important

so we have no AAA SSS or SAS here... or do we?

4. ## Re: length of a line inside a triangle, given all sides

Originally Posted by ketanco
yes thats what i meant....
by the way not O, but D.. not important

so we have no AAA SSS or SAS here... or do we?
Yes you do. Angle B is common. The other sides are in the same ratio ( you might find that easier to see if you draw tri DBE as is and then draw tri CBA with C at the top).

Remember the S's in SAS mean that the sides (forming the A) are in the ratio. (If they were equal, the triangles would be congruent)