English

Draw an Isosceles Triangle with Base 5 Cm and Height 4 Cm. Draw a Triangle Similar to the Triangle Drawn Whose Sides Are 2 3 Times the Sides of the Triangle. - Geometry Mathematics 2

Advertisements
Advertisements

Question

Draw an isosceles triangle with base 5 cm and height 4 cm. Draw a triangle similar to the triangle drawn whose sides are `2/3` times the sides of the triangle.

Solution

shaalaa.com
  Is there an error in this question or solution?
2018-2019 (March) Balbharati Model Question Paper Set 2

RELATED QUESTIONS

In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC

If AD = 4, AE = 8, DB = x – 4, and EC = 3x – 19, find x.


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.


In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC

If AD = 2 cm, AB = 6 cm and AC = 9 cm, find AE.


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.


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.


If D and E are points on sides AB and AC respectively of a ΔABC such that DE || BC and BD = CE. Prove that ΔABC is isosceles.


D and E are the points on the sides AB and AC respectively of a ΔABC such that: AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm. Prove that BC = 5/2 DE.


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. Find the value of x, when

AD = 4cm, DB = (x – 4) cm, AE = 8cm and EC = (3x – 19) cm.  


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.  

 


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 fig., line BC || line DE, AB = 2, BD = 3, AC = 4 and CE = x, then find the value of x


A line is parallel to one side of triangle which intersects remaining two sides in two distinct points then that line divides sides in same proportion.

Given: In ΔABC line l || side BC and line l intersect side AB in P and side AC in Q.

To prove: `"AP"/"PB" = "AQ"/"QC"`

Construction: Draw CP and BQ

Proof: ΔAPQ and ΔPQB have equal height.

`("A"(Δ"APQ"))/("A"(Δ"PQB")) = (["______"])/"PB"`   .....(i)[areas in proportion of base]

`("A"(Δ"APQ"))/("A"(Δ"PQC")) = (["______"])/"QC"`  .......(ii)[areas in proportion of base]

ΔPQC and ΔPQB have [______] is common base.

Seg PQ || Seg BC, hence height of ΔAPQ and ΔPQB.

A(ΔPQC) = A(Δ______)    ......(iii)

`("A"(Δ"APQ"))/("A"(Δ"PQB")) = ("A"(Δ "______"))/("A"(Δ "______"))`   ......[(i), (ii), and (iii)]

`"AP"/"PB" = "AQ"/"QC"`   .......[(i) and (ii)]


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 = [______]


In ΔABC, AB = 6 cm and DE || BC such that AE = `1/4` AC then the length of AD 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 the given figure, PQ || AC. If BP = 4 cm, AP = 2.4 cm and BQ = 5 cm, then length of BC is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×