In figure, find the value of x which will make DE || AB?
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IIUnicornPrincessII:
2 is the answer
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Answered by
284
BASIC PROPORTIONALITY THEOREM (BPT) : 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. That is also known as Thales theorem.
GIVEN:
In ∆ABC , DE || AB
AD= 3x+19, DC= x+3, BE= 3x+4, EC = x
AD /DC = BE/EC
[ By Thales theorem(BPT)]
3x+19/x+3 = 3x+4/x
(3x+19) × x = (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= 2
x = 2
Hence, the value of x is 2 .
HOPE THIS WILL HELP YOU...
GIVEN:
In ∆ABC , DE || AB
AD= 3x+19, DC= x+3, BE= 3x+4, EC = x
AD /DC = BE/EC
[ By Thales theorem(BPT)]
3x+19/x+3 = 3x+4/x
(3x+19) × x = (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= 2
x = 2
Hence, the value of x is 2 .
HOPE THIS WILL HELP YOU...
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Answered by
43
Answer:If DE∣∣AB, then ΔCDE∼ΔABC
By property of similar triangles:
CD/=CE/BC
x+3/4x+22=x/4x+4
Cross-multiplying:
(x+3)(4x+4)=x(4x+22)
4x2+16x+12=4x2+22x
12=6x
⟹x=2
Step-by-step explanation:
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