English

In the following figure, in Δ PQR, seg RS is the bisector of ∠PRQ. PS = 3, SQ = 9, PR = 18. Find QR. - Geometry Mathematics 2

Advertisements
Advertisements

Question

In the following figure, in Δ PQR, seg RS is the bisector of ∠PRQ.

PS = 3, SQ = 9, PR = 18. Find QR.

Solution

SR is the bisector of ∠R.

`"RP"/"PS"="QR"/"SQ"`

`rArr18/3="QR"/9`

`therefore"QR"=54"cm"`

 

shaalaa.com
  Is there an error in this question or solution?
2014-2015 (March) Set B

RELATED QUESTIONS

The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB


P and Q are points on sides AB and AC respectively of ∆ABC. If AP = 3 cm, PB = 6cm. AQ = 5 cm and QC = 10 cm, show that BC = 3PQ.


In ∆ABC, DE is parallel to base BC, with D on AB and E on AC. If `\frac{AD}{DB}=\frac{2}{3}` , find `\frac{BC}{DE}.`


Given: ∠GHE = ∠DFE = 90°,

DH = 8, DF = 12,

DG = 3x – 1 and DE = 4x + 2.


Find: the lengths of segments DG and DE.


In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form: 

 


In a circle, two chords AB and CD intersect at a point P inside the circle. Prove that
(a) ΔPAC ∼PDB (b) PA. PB= PC.PD  

 


A ship is 400m laig and 100m wide. The length of its model is 20 cm. find the surface area of the deck of the model. 


In figure, PQ is parallel to BC, AP : AB = 2 : 7. If QC = 0 and BC = 21,

Find
(i) AQ
(ii) PQ


ΔABC has been reduced by a scale factor 0.6 to ΔA'B'C'/ Calculate:Length of B' C', if BC = 8cm


ΔABC is enlarged, with a scale factor 5. Find: BC, f B'C' = 16cm


The dimensions of the model of a building are 1.2m x 75cm x 2m. If the scale factor is 1 : 20; find the actual dimensions of the building.


On a map drawn to a scale of 1:25000, a triangular plot of land is right angled and the sides forming the right angle measure 225cm and 64cm.Find: The area of the plot in sq. km.


In the adjacent figure, ∆ACB ~ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ


If figure OPRQ is a square and ∠MLN = 90°. Prove that QR2 = MQ × RN


If ∆ABC ~ ∆DEF such that area of ∆ABC is 9 cm2 and the area of ∆DEF is 16 cm2 and BC = 2.1 cm. Find the length of EF.


D is the mid point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that b2 = `"p"^2 + "a"x + "a"^2/4`


D is the mid point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that c2 = `"p"^2 - "a"x + "a"^2/4`


In the given figure, if ΔEAT ~ ΔBUN, find the measure of all angles.


ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC is half of OA.


In figure, if AD = 6cm, DB = 9cm, AE = 8cm and EC = 12cm and ∠ADE = 48°. Find ∠ABC.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×