Answer:
X = 5
Step-by-step explanation:
Given : In ΔACE
B is the midpoint of AC i.e. AB=AC
D is the midpoint of CE i.e. ED=DC
BD = 3x +5
AE = 4x +20
Proof : To find value of x we will use mid segment theorem i.e. The line connected by the midpoints of two sides of a triangle is parallel to the third side and is also half of the third side .
⇒[tex]\frac{1}{2} AE = BD[/tex]
⇒[tex]\frac{1}{2} 4x+20 = 3x+5[/tex]
⇒[tex]4x+20=2(3x+5)[/tex]
⇒[tex]4x+20=6x+10[/tex]
⇒[tex]20-10=6x-4x[/tex]
⇒[tex]10=2x[/tex]
⇒[tex]\frac{10}{2} = x[/tex]
⇒ [tex]5=x[/tex]
So, the value of x is 5
hjgh
The value of x for the given equations is 5.
Given data:
In triangle ACE, AC is a side of triangle, such B is the midpoint of AC. So, AB = AC.
CE is another side of triangle such that D is the midpoint of CE. So, ED = DC.
Also,
BD = 3x + 5 (BD is the base of triangle formed by joining the mid-point)
AE = 4x + 20 (AE is the base of triangle ACE)
To find value of x we will use mid point theorem i.e. The line connected by the midpoints of two sides of a triangle is parallel to the third side and is also half of the third side .
Therefore,
[tex]BD=\dfrac{1}{2} AE\\\\3x+5=\dfrac{1}{2} (4x+20)\\\\3x+5=2x+10\\\\x=5[/tex]
Thus, we can conclude that the value of x is 5.
Learn more about the mid-point theorem here:
https://brainly.com/question/17200698
