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Solve for X enter your answer in the box

Solve For X Enter Your Answer In The Box class=

Sagot :

xenia168

Answer:

x = 6

Step-by-step explanation:

View image xenia168
Tekashii

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 :-

  • Value of x

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]

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