in triangle abc De parallel to BC ad is equal to BD is equal to x minus 2 Y is equal to X + 2 is equal to x minus 1 find the value of x in the given figure
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Answer:
x = 1 or -1/2
Step-by-step explanation:
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russian43
12.10.2019
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in the given figure in triangle abc De is parallel to BC show that ad equal to 4 minus 3 equal to 8 x minus 7 cm BD equal to 3 x minus 1 cm and c equal to 5 x minus 3 cm find value of x
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Hi there,
There are some missing data in the question above. I am writing the complete question and also attaching the image below and thereby solving it accordingly. Hoping the complete question to be as follows:
Q. In the given figure in triangle ABC, DE parallel BC. If AD= (4x-3), AE =(8x-7)cm, BD = (3x-1) cm and CE = 5x-3 cm. Find the value of x.
Answer: x = 1 or -1/2
Step-by-step explanation:
Let’s consider ∆ ABC,
DE // BC [given]
Since if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line will divide those two sides proportionally. This theorem is also called as side splitter theorem.
∴ \frac{AD}{BD} = \frac{AE}{CE}
On substituting the given values of AD, BD, AE & CE, we get
⇒ \frac{4x-3}{3x-1} = \frac{8x-7}{5x-3}
⇒ 20x² -15x -12x + 9 = 24x² - 8x - 21x + 7
⇒ 20x² - 27x + 9 = 24x² – 29x + 7
⇒ 4x² - 2x – 2 = 0
⇒ 4x² - 4x + 2x – 2 = 0
⇒ 4x(x-1) + 2(x-1) = 0
⇒ (4x+2)(x-1) = 0
⇒ (4x+2) = 0 or (x-1) = 0
⇒ x = -1/2 or x = 1
Thus, the value of x is 1 or (-1/2).
Answer:
BD is equal to
AB/DB=AE/EC
4/DB=6/3
2 divides 4 and 6 leave 2 and 3
3 divide 3 leave 1
2 multiple 1 is equal 2