What values of x will make DE || AB in the given figure?
Answers
SOLUTION :
BASIC PROPORTIONALITY THEOREM (BPT) is used in this question .
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
This theorem also known as ‘Thales theorem’.
Given :
DE || AB
Then,
CE / EB = CD / DA
[By BPT]
x/ 3x+4 = x+3 / 3x+19
x(3x+19) = (3x+4) (x+3)
3x² + 19x = 3x² + 9x + 4x +12
3x² + 19x = 3x² + 13x +12
3x² - 3x² + 19x -13x = 12
6x = 12
x = 12/6
x = 2
Hence, the value of x is 2.
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Answer:
Step-by-step explanation:
Given :-
DE || AB
AD = 3x + 19
DC = x + 3
BE = 3x + 4
To Find :-
Value of x
Formula to be used :-
Thales theorem i.e CE/EB = CD/DA
Solution :-
Putting all values, we get
CE/EB = CD/DA
⇒ x/3x + 4 = x + 3/3x + 19
⇒ x(3x + 19) = (3x + 4) (x + 3)
⇒ 3x² + 19x = 3x² + 9x + 4x +12
⇒ 3x² + 19x = 3x² + 13x +12
⇒ 3x² - 3x² + 19x -13x = 12
⇒ 6x = 12
⇒ x = 12/6
⇒ x = 2
Hence, The value os x is 2.
Extra Information :-
Thales theorem :-
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.