Advertisements
Advertisements
Question
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 4 cm, DB = 4.5 cm and AE = 8 cm, find AC.
Solution
We have,
DE || BC
Therefore, by basic proportionality theorem, we have,
`"AD"/"DB"="AE"/"EC"`
`rArr4/4.5=8/"EC"`
`rArr"EC"=(8xx4.5)/4`
⇒ EC = 9cm
Now, AC = AE + EC
= 8 + 9
= 17 cm
∴ AC = 17 cm
APPEARS IN
RELATED QUESTIONS
In the given figure, D is a point on side BC of ΔABC such that ∠ADC=∠BAC . Prove that AD is the bisector of ∠BAC.
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC. Find the value of x, when
AD = x cm, DB = (x – 2) cm, AE = (x + 2) cm and EC = (x – 1) cm.
ΔABC is am equilateral triangle of side 2a units. Find each of its altitudes.
Find the length of each side of a rhombus whose diagonals are 24cm and 10cm long.
In ΔABC, AB = AC. Side BC is produced to D. Prove that `AD^2−AC^2`= BD.CD
In the given figure, in ∆ABC, point D on side BC is such that, ∠BAC = ∠ADC. Prove that, CA2 = CB × CD
From fig., seg PQ || side BC, AP = x + 3, PB = x – 3, AQ = x + 5, QC = x – 2, then complete the activity to find the value of x.
In ΔPQB, PQ || side BC
`"AP"/"PB" = "AQ"/(["______"])` ...[______]
`(x + 3)/(x - 3) = (x + 5)/(["______"])`
(x + 3) [______] = (x + 5)(x – 3)
x2 + x – [______] = x2 + 2x – 15
x = [______]
State and prove Basic Proportionality theorem.
