In a ∆ABC, D and E are points on the sides AB and AC respectively such that DE || BC.
(i) If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If AD/DB = 3/4 and AC = 15 cm, find AE.
(iii) If ADDB=2/3 and AC = 18 cm, find AE.
Answers
BASIC PROPORTIONALITY THEOREM (BPT) :
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
SOLUTION :
1) Given : Δ ABC & DE || BC ,
AD = 6 cm, DB = 9 cm and AE = 8 cm.
Let EC =x cm
So, AD/DB=AE/ EC
[By using basic proportionality Theorem]
6/ 9 = 8/x
6x = 9 × 8
6x = 72 cm
x = 72/6 cm
x = 12 cm
AC = AE + EC
AC = 8 + 12
AC = 20 cm
Hence, the length of AC is 20 cm.
2) Given : Δ ABC & DE || BC , AD/BD = 3/4 and AC = 15 cm
Let, AE = x cm
EC = AC - AE
EC = 15 - x
So, AD/DB=AE/ EC
[By using basic proportionality Theorem]
Then, 3/4=x/15–x
3(15 - x) = 4x
45 - 3x = 4x
-3x - 4x = - 45
7x = 45
x = 45/7
x = 6.43 cm
Hence, the length of AE is 6.43 cm.
3)Given : Δ ABC & DE || BC ,AD/BD = ⅔ and AC = 18 cm
Let, AE = x cm
EC = AC - AE
EC = 18 - x
So, AD/DB = AE/ EC
[By using basic proportionality Theorem]
Then, 2/3=x/18 - x
3x = 2(18 - x)
3x = 36 – 2x
3x + 2x = 36
5x = 36 cm
x = 36/5 cm
x = 7.2 cm
Hence, the length of AE is 7.2 cm
HOPE THIS ANSWER WILL HELP YOU...
(1) In triangleABC
DEparallel toBC
so,by Thales'Theorem