Question

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​

Answer 1

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).

Hope this is helpful!!!!

Answer 2

Step-by-step explanation:

hope this helps your study