Answer:
x = 6
Step-by-step explanation:
GIVEN :-
- AD ║ BC
- AE = 16 units
- AB = 5x + 2 units
- DE = 12 units
- DC = 24 units
TO FIND :-
GENERAL CONCEPT TO BE USED IN THIS QUESTION :-
Basic Proportionality Theorem -
If a line drawn parallel to one side of a triangle and intersects the other two sides at distinct points , it divides the other two sides in equal proportion.
SOLUTION :-
AD is the line drawn parallel to BC and intersects EB & EC at A & D respectively. By using Basic Proportionality Theorem , it can be stated that -
[tex]\frac{AE}{AB} = \frac{DE}{DC}[/tex]
[tex]=> \frac{16}{5x + 2} = \frac{12}{24}[/tex]
[tex]=> \frac{16}{5x + 2} = \frac{1}{2}[/tex]
[tex]=> 5x + 2 = 16 \times 2 = 32[/tex]
[tex]=> 5x = 32 - 2 = 30[/tex]
[tex]=> x = \frac{30}{5} = 6[/tex]
