Advertisements
Advertisements
प्रश्न
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 8x − 7, DB = 5x − 3, AE = 4x − 3 and EC = (3x − 1), find the value of x.
उत्तर
We have,
DE || BC
Therefore, by basic proportionality theorem, we have,
`"AD"/"DB"="AE"/"EC"`
`rArr(8x-7)/(5x-3)=(4x-3)/(3x-1)`
⇒ (8x − 7)(3x − 1) = (4x − 3)(5x − 3)
⇒ 24x2 − 8x − 21x + 7 = 20x2 − 12x − 15x + 9
⇒ 24x2 − 20x2 − 29x + 27x + 7 − 9 = 0
⇒ 4x2 − 2x − 2 = 0
⇒ 2[2x2 − x − 1] = 0
⇒ 2x2 − x − 1 = 0
⇒ 2x2 − 2x + 1x − 1 = 0
⇒ 2x(x − 1) + 1(x − 1) = 0
⇒ (2x + 1) (x – 1) = 0
⇒ 2x + 1 = 0 or x – 1 = 0
⇒ x = −1/2 or x = 1
𝑥 = −1/2 is not possible
∴ x = 1
संबंधित प्रश्न
In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that `(QS)/(SR) = (PQ)/(PR)`
In a ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC
AB = 2cm, AD = 8cm, AE = 12 cm and AC = l8cm.
In a ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC
AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.
In a ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC
AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm.
In a ΔABC, D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4cm, AE = 3.2 cm, DE = 2cm and BC = 5 cm, find BD and CE.
M and N are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether MN || QR
PM = 4cm, QM = 4.5 cm, PN = 4 cm and NR = 4.5 cm
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.
If `(AD)/(DB) = 4/7` and AC = 6.6cm, find AE.
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.
If` (AD)/(AB) = 8/15 and EC = 3.5cm`, find AE.
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.
In the given figure, ABCD is a trapezium in which AB║DC and its diagonals intersect at O. If AO = (5x – 7), OC = (2x + 1) , BO = (7x – 5) and OD = (7x + 1), find the value of x.
In the given figure, side BC of a ΔABC is bisected at D
and O is any point on AD. BO and CO produced meet
AC and AB at E and F respectively, and AD is
produced to X so that D is the midpoint of OX.
Prove that AO : AX = AF : AB and show that EF║BC.
ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ = `1/4` AC. If PQ produced meets BC at R, prove that R is the midpoint of BC.
In the adjoining figure, ABC is a triangle in which AB = AC. IF D and E are points on AB and AC respectively such that AD = AE, show that the points B, C, E and D are concyclic.
A guy wire attached to a vertical pole of height 18 m is 24m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
In the given figure, O is a point inside a ΔPQR such that ∠PQR such that ∠POR = 90°, OP = 6cm and OR = 8cm. If PQ = 24cm and QR = 26cm, prove that ΔPQR is right-angled.
Find the length of altitude AD of an isosceles ΔABC in which AB = AC = 2a units and BC = a units.
ΔABC is am equilateral triangle of side 2a units. Find each of its altitudes.
Find the length of a diagonal of a rectangle whose adjacent sides are 30cm and 16cm.
An aeroplane leaves an airport and flies due north at a speed of 1000km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after` 1 1/2` hours?
In a ABC , AD is a median and AL ⊥ BC .
Prove that
(a) `AC^2=AD^2+BC DL+((BC)/2)^2`
(b) `AB^2=AD^2-BC DL+((BC)/2)^2`
(c) `AC^2+AB^2=2.AD^2+1/2BC^2`
In Δ PQR, points S and T
are the midpoints of sides PQ
and PR respectively.
If ST = 6.2 then find the length of QR.
Prove that, if a line parallel to a side of a triangle intersects the other sides in two district points, then the line divides those sides in proportion.
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 = [______]
ΔABC ~ ΔDEF. If AB = 4 cm, BC = 3.5 cm, CA = 2.5 cm and DF = 7.5 cm, then the perimeter of ΔDEF is ______.
In the given figure ΔABC ~ ΔPQR, PM is median of ΔPQR. If ar ΔABC = 289 cm², BC = 17 cm, MR = 6.5 cm then the area of ΔPQM is ______.
 |
 |
In figure, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find PQ, QR and RS.
In figure, line segment DF intersect the side AC of a triangle ABC at the point E such that E is the mid-point of CA and ∠AEF = ∠AFE. Prove that `(BD)/(CD) = (BF)/(CE)`.
