Question

maths class 10th plz answer this​

Answer 1

Answer:

c) 3

Step-by-step explanation:

DE||BC,

x = x+3

x+1 x+5

x²+5x=(x+1) (x+3)

x²+5x= x²+3x+x+3

5x=4x+ 3

5x-4x=3

x=3

Answer 2

Basic Proportionality

Theorem

A straight line drawn parallel to a side of triangle intersecting the other two sides, divides the sides in the same ratio.

Now, Let's move on finding the solution for our question.

In ΔABC, we have $\sf{DE\:||\:BC}$

By Basic Proportionality Theorem,

We get $\sf{\dfrac{AD}{DB}}\:=\:{\dfrac{AE}{EC}}$

Substituting values, we get,

$\implies\sf{\dfrac{x}{x\:+\:1}}\:=\:{\dfrac{x\:+\:3}{x\:+\:5}}$

$\implies\sf{x\:(x\:+\:5)\:=\:(x\:+\:3)\:(x\:+\:1)}$

$\implies\sf{x^2\:+\:5x\:=\:x^2\:+\:x\:+\:3x\:+\:3}$

$\implies\sf{x^2\:+\:5x\:-\:x^2\:-\:x\:-\:3x\:-\:3\:=\:0}$

$\implies\sf{{\cancel{x^2}}\:+\:5x\:-\:{\cancel{x^2}}\:-\:x\:-\:3x\:-\:3\:=\:0}$

$\implies\sf{5x\:-\:x\:-\:3x\:-\:3\:=\:0}$

$\implies\sf{2x\:-\:x\:-\:3\:=\:0}$

$\implies\sf{x\:-\:3\:=\:0}$

$\implies\sf{x\:=\:3}$

The value of of x is = 3.

Hence, the correct option is = (c) 3.

$\rule{90mm}{2pt}$

Important Notes :

$\boxed{\begin{array}{l}\rm{In \: \triangle ABC \textsf{,} \: let \: DE \| BC. \: Then\textsf{,}}\\ \\ \rm{(i) \: \: \dfrac{AD}{DB} = \dfrac{AE}{EC}} \\ \\ \rm{(ii) \: \: \dfrac{AB}{DB} = \dfrac{AC}{EC}} \\ \\ \rm{(iii) \: \: \dfrac{AD}{AB} = \dfrac{AE}{AC}} \end{array}}$