Question

Assertion: D and E are points on the sides AB and AC respectively of a triangle ABC such that DE is parallel to BC then the value of x is 4, when AD= x cm, DB= (x-2) cm, AE= (x+2) cm and EC= (x-1) cm.
Reason: If a line is parallel to one side of a triangle then it divides the other two sides in the same ration.

a) Both assertion and reason are true and reason is the correct explanation of assertion.
b) Both assertion and reason are true but reason is not the correct explanation of assertion.
c) Assertion is true but reason is false
d) Assertion is false but reason is true

PLS GIVE ANSWER FAST

Answer 1

Step-by-step explanation:

option d is the correct answer

Answer 2

Answer:

Assertion/Reasoning

Step-by-step explanation:

• The Assertion Statement given is:

D and E are points on the sides AB and AC respectively of a triangle ABC such that DE is parallel to BC then the value of $x$ is $4$, when $AD=x$ cm, $DB=(x-2)$ cm, $AE=(x+2)$ cm and $EC=(x-1)$ cm.

• The Reason given is:

If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio.

The reason is true.

• Suppose ABC is a triangle and DE is the line parallel to AC, then

                   Δ$ADE$≈Δ$ABC$        (by AA Similarity Criteria)

That means, the corresponding sides are in the same ratio.

Therefore,

                                       $\frac{AD}{AB}=\frac{AE}{AC}$

This proves that, if a line is parallel to one side of a triangle then it divides the other two sides in the same ratio.

That means, the reason given is true.

• Now, the reason given is true for the assertion statement because according to the reason given, we can say that

                                                $\frac{AD}{AB}=\frac{AE}{AC}$

                                                $\frac{x}{AD+DB}=\frac{x+2}{AE+EC}\\\frac{x}{x+x-2}=\frac{x+2}{x+2+x-1}\\\frac{x}{2x-2}=\frac{x+2}{2x+1}\\x(2x+1)=(x+2)(2x-2)\\2x^2+x=2x^2-2x+4x-4\\x+2x-4x=-4\\-x=-4\\x=4$

Therefore, the assertion statement is true.

Hence, we can say that both assertion and reason are true and reason is the correct explanation of assertion.

Therefore, option (a) is correct.