B is the midpoint of and D is the midpoint of . Solve for x, given BD = 3x + 5 and AE = 4x + 20.
https://www.connexus.com/content/media/464267-1132011-72634-PM-1941616734.png

Question

B is the midpoint of  and D is the midpoint of . Solve for x, given BD = 3x + 5 and AE = 4x + 20. 
https://www.connexus.com/content/media/464267-1132011-72634-PM-1941616734.png

ash2326 · Answer

B is the mid point of AC and D is the mid point of CE
In triangles CBD and CAE
CB/CA=1/2
CD/CE=1/2
angle C is the common angle
so these two triangles are similar
therefore all angles are equal , and all triangles are in the same ratio
hence BD/AE=1/2
BD=3x+5
AE=4x+20
3x+5/(4x+20)=1/2
6x+10=4x+20
2x=10
x=5

anonymous · Answer

thank you!!!