Advertisements
Advertisements
Question
The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5cm, find the length of QR.
Solution
It is given that Δ ABC ~ Δ PQR
Therefore, the ration of the areas of triangles will be equal to the ratio of squares of their corresponding sides.
`(ar(ΔABC))/(ar(ΔPQR))=(BC^2)/(QR^2)`
⇒` 9/16=4^2/(QR^2)`
⇒` QR^2=(4.5xx4.55xx16)/9`
⇒ `QR= (sqrt(4.5xx4.5xx16))/9`
`= (4.5xx4)/3`
= 6 cm
Hence, QR = 6 cm
APPEARS IN
RELATED QUESTIONS
See the given figure. DE || BC. Find EC.
E and F are points on the sides PQ and PR, respectively, of a ΔPQR. For the following case, state whether EF || QR.
PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
`triangleDEF ~ triangleMNK`. If DE = 5 and MN = 6, then find the value of `(A(triangleDEF))/(A(triangleMNK))`
In the figure, PQRS is a parallelogram with PQ = 16 cm and QR = 10 cm. L is a point on PR such that RL : LP = 2 : 3. QL produced meets RS at M and PS produced at N.
Find the lengths of PN and RM.
In the figure, given below, the medians BD and CE of a triangle ABC meet at G. Prove that:
- ΔEGD ~ ΔCGB and
- BG = 2GD from (i) above.
A vertical pole of length 7.5 cm casts a shadow 5 m long on the ground and at the same time a tower casts a shadow 24 m long. Find the height of the tower.
In the given figure, ∠1 = ∠2 and `(AC)/(BD)=(CB)/(CE)` Prove that Δ ACB ~ Δ DCE.
ABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the midpoints of AB, AC, CD and BD respectively, show that PQRS is a rhombus.
In ∆ABC, ray BD bisects ∠ABC and ray CE bisects ∠ACB. If seg AB ≅ seg AC then prove that ED || BC.
Δ ABC ~ Δ DEF. If BC = 3cm , EF=4cm and area of Δ ABC = 54 cm2 , find area of Δ DEF.
Δ ABC is similar to Δ PQR. If AB = 6cm, BC = 9cm, PQ = 9cm and PR = 10.5cm, find the lengths of AC and QR.
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.
The scale of a map is 1 : 200000. A plot of land of area 20km2 is to be represented on the map. Find
The area on the map that represents the plot of land.
A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find : OC', if OC = 21 cm.
Also, state the value of :
- `(OB^')/(OB)`
- `(C^'A^')/(CA)`
A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find : BC, if B' C' = 15 cm.
A model of an aeroplane is made to a scale of 1 : 400. Calculate : the length, in m, of the aeroplane, if length of its model is 16 cm.
In the following figure, point D divides AB in the ratio 3 : 5. Find : `(AD)/(AB)`
In ΔPQR, L and M are two points on the base QR, such that ∠LPQ = ∠QRP and ∠RPM = ∠RQP.
Prove that : (i) ΔPQL ∼ ΔRPM
(ii) QL. Rm = PL. PM
(iii) PQ2 = QR. QL.
In ΔABC, point D divides AB in the ratio 5:7, Find: `"AE"/"EC"`
AM and DN are the altitudes of two similar triangles ABC and DEF. Prove that: AM : DN = AB : DE.
Prove that the external bisector of an angle of a triangle divides the opposite side externally n the ratio of the sides containing the angle.
The areas of two similar triangles are 16cm2 and 9cm2 respectively. If the altitude of the smaller triangle is 1.8cm, find the length of the altitude corresponding to the larger triangle.
The areas of two similar triangles are 169cm2 and 121cm2 respectively. If one side of the larger triangle is 26cm, find the length of the corresponding side of the smaller triangle.
D and E are points on the sides AB and AC of ΔABC such that DE | | BC and divides ΔABC into two parts, equal in area. Find `"BD"/"AB"`.
Find the scale factor in each of the following and state the type of size transformation:
Image length = 6cm, Actual length = 4cm.
Two triangles QPR and QSR, right angled at P and S respectively are drawn on the same base QR and on the same side of QR. If PR and SQ intersect at T, prove that PT × TR = ST × TQ
In the figure, if ∠FEG ≡ ∠1 then, prove that DG2 = DE.DF
In the given figure ΔABC ~ ΔPQR. The value of x is
 |
 |
In the figure PQ || BC. If `"PQ"/"BC" = 2/5` then `"AP"/"PB"` is ______.
In a square of side 10 cm, its diagonal = ______.
