Answer:
The value of x is 5.
Step-by-step explanation:
Label the diagram such as
Given:
AD= x
DB= x +5
AE = x - 2
EC = x + 1
DE || BC
To Find:
x = ?
Solution:
Basic Proportionality Theorem:
"If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".
DE || BC
∴ [tex]\dfrac{AD}{DB}= \dfrac{AE}{EC}[/tex] ...Basic Proportionality Theorem
Substituting the values in it we get
[tex]\dfrac{x}{x+5}= \dfrac{x-2}{x+1}\\x(x+1)=(x+5)(x-2)\\\\x^{2}+x= x^{2}+3x-10\\ -2x=-10\\\\x=\dfrac{10}{2}=5\\ \\\therefore x =5[/tex]
The value of x is 5.
