Assertion : D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC then the value of a is 8, when AD=a cm, DB=(a–4) cm, AE=(a+4) cm and EC = (a –2) cm. Reason :If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio (a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b)Both assertion(A) and reason(R) are true but reason(R)is not the correct explanation of assertion (A)ion 2 (c)Assertion (A) is true but reason (R) is false. (d)Assertion (A) is false but reason (R) is true. MCQ question answer
Answers
Answer:
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Step-by-step explanation:
Given : AD=4 cm,DB=(x−4) cm,AE=8 cm and EC=(3x−19) cm.
To Find : x
We know that, by BPT(Basic proportionality theorem)
DB
AD
=
EC
AE
(x−4)
4
=
(3x−19)
8
4(3x−19)=8(x−4)
12x−76=8x−32
Solving, we get
- Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Given :-
Assertion :- D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC then the value of a is 8, when AD = a cm, DB = (a – 4) cm, AE = (a+4) cm and EC = (a – 2) cm.
Reason :- If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio .
To Find :-
a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion(A) and reason(R) are true but reason(R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Solution :-
from image we can see that, D and E are points on the sides AB and AC respectively of a ΔABC and DE is parallel to BC .
Also,
→ AD = a cm
→ DB = (a - 4) cm
→ AE = (a + 4) cm
→ EC = (a - 2) cm
now, since DE || BC .
→ AD/DB = AE/EC { If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio }
→ a/(a - 4) = (a + 4)/(a - 2)
→ a(a - 2) = (a - 4)(a + 4)
→ a² - 2a = (a)² - (4)²
→ a² - 2a = a² - 16
→ (-2a) = (-16)
→ a = 8
therefore, value of a is equal to 8 .
Conclusion :-
- Assertion (A) is true .
- Reason (R) is true .
- Reason (R) is the correct explanation of assertion (A).
Hence, Option (a) is correct answer .
Extra knowledge :-
Proof :- If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio .
In ∆ADE and ∆ABC we have,
→ ∠ADE = ∠ABC { since DE || BC , corresponding angles are equal. }
→ ∠DAE = ∠BAC { common }
So,
→ ∆ADE ~ ∆ABC { By AA similarity }
then,
→ AD/AB = AE/AC { When two ∆'s are similar their corresponding sides are in same ratio. }
→ AB/AD = AC/AE
subtracting 1 from both sides ,
→ (AB/AD) - 1 = (AC/AE) - 1
→ (AB - AD)/AD = (AC - AE)/AE
→ DB/AD = EC/AE
→ AD/DB = AE/AC { Proved. }
Learn more :-
In the given figure PQ || RS || BC. If RS = 4 cm, PQ = 3 cm, then BC is equal to https://brainly.in/question/45600047
Which of these can never be the ratio of the sides of the triangle? a. 3:5:7 b. 3:5:3 C. 2:2:3 d. 2:5:8
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