In a ∆ABC, D and E are points on the sides AB and AC respectively such that DE || BC.
(iv) If AD = 4, AE = 8, DB = x − 4, and EC = 3x − 19, find x.
(v) If AD = 8 cm, AB = 12 cm and AE = 12 cm, find CE.
(vi) if AD = 4 cm, DB = 4.5 cm and AE = 8 cm, find AC.
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 :
4) Given : Δ ABC & DE || BC ,AD = 4 cm, AE = 8 cm, DB = x – 4 and EC = 3x – 19
So, AD/DB=AE/ EC
[By using basic proportionality Theorem]
Then, 4/ (x - 4) = 8 / (3x–19)
4(3x – 19) = 8(x – 4)
12x – 76 = 8x - 32
12x – 8x = – 32 + 76
4x = 44 cm
x = 11 cm
Hence, the value of x is 11 cm.
5) Given : Δ ABC & DE || BC , AD = 8 cm, AB = 12 cm, and AE = 12 cm.
DB = AB - AD
DB = 12 - 8
DB = 4 cm
So, AD/DB = AE/ EC
[By using basic proportionality Theorem]
Then, 8/4=12/CE
8CE = 4 × 12
CE = (4 × 12)/8
CE = 12/2
CE = 6 cm
Hence, the length of CE is 6 cm
6) Given : Δ ABC & DE || BC , AD = 4 cm, DB = 4.5 cm, AE = 8 cm
So, AD/DB=AE/ EC
[By using basic proportionality Theorem]
Then, 4/4.5 = 8/EC
EC =( 4.5 × 8) /4
EC = 4.5 × 2
EC = 9 cm
AC = AE + EC
AC = 8 + 9
AC = 17 cm
Hence, the length of AC is 17 cm.
HOPE THIS ANSWER WILL HELP YOU...
4) By basic proposnality theorem....
AD/DB = AE/EC
WHERE AD=4 AE =8 DB=X-4 EC=3X-19
SO substitute the value...
We get
4/x-4 = 8/3x-19. ( Cross multiply)
4(3x-19)= 8(x-4)
12x-76=8x-32
12x-8x=-32+76
4x=44
x=11
5) AD 8cm. AB 12 AE 12 CE?
AB 12cm DB=4cm
AD/DB=AE/EC
8/4=12/EC
EC=6cm...