Advertisements
Advertisements
प्रश्न
It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`. Then, `(ar(PRQ))/(ar(BCA))` is equal to ______.
पर्याय
9
3
`1/3`
`1/9`
उत्तर
It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`. Then, `(ar(PRQ))/(ar(BCA))` is equal to 9.
Explanation:
Given, ∆ABC ~ ∆PQR and `("BC")/("QR") = 1/3`
We know that, the ratio of the areas of two similar triangles is equal to square of the ratio of their corresponding sides.
∴ `("ar(∆PRQ)")/("ar(∆BCA)") = ("QR")^2/("BC")^2 = (("QR")/("BC"))^2`
= `(3/1)^2`
= `9/1`
= 9
APPEARS IN
संबंधित प्रश्न
In the following figure, seg DH ⊥ seg EF and seg GK ⊥ seg EF. If DH = 18 cm, GK = 30 cm and `A(triangle DEF) = 450 cm^2`, then find:
1) EF
2) `A(triangle GFE)`
3) `A(square DFGE)`
In ΔABC and ΔDEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE=10cm, EF = 8 cm and FD = 8.4 cm. If AL ⊥ BC and DM ⊥ EF, find AL: DM.
State, true or false:
All isosceles triangles are similar.
In the given figure, ABC is a triangle. DE is parallel to BC and `(AD)/(DB) = 3/2`.
- Determine the ratios `(AD)/(AB)` and `(DE)/(BC)`.
- Prove that ∆DEF is similar to ∆CBF. Hence, find `(EF)/(FB).`
- What is the ratio of the areas of ∆DEF and ∆BFC?
A model of a ship if made to a scale of 1 : 200.
(i) Thelength of the model is 4 m; calculate the length of the ship.
(ii) The area of the deck of the ship is 160000 m2; find the area of the deck of the model.
(iii) The volume of the model is 200 litres; calculate the volume of the ship in m3.
In the given figure, triangle ABC is similar to triangle PQR. AM and PN are altitudes whereas AX and PY are medians.
prove that
`("AM")/("PN")=("AX")/("PY")`
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 the given figure, if ∠ADE = ∠B, show that ΔADE ~ ΔABC. If AD = 3.8cm, AE = 3.6cm, BE = 2.1cm and BC = 4.2cm, find DE.
State the SAS-similarity criterion
Are the triangles in the given figure similar? If yes, by which test?
As shown in figure, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time?
If Δ ABC , MN || BC .
If AN : AC= 5 : 8, find ar(Δ AMN) : ar(Δ ABC)
In Δ PQR, MN is drawn parallel to QR. If PM = x, MQ = (x-2), PN = (x+2) and NR = (x-1), find the value of x.
In Δ ABC, D and E are points on the sides AB and AC respectively. If AD= 4cm, DB=4.Scm, AE=6.4cm and EC=7.2cm, find if DE is parallel to BC or not.
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 in km2 that can be represented by 1 cm2
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 cm, of the model; if the length of the aeroplane is 40 m.
In the following figure, point D divides AB in the ratio 3 : 5. Find :
- `(AE)/(EC)`
- `(AD)/(AB)`
- `(AE)/(AC)`
Also, if: - DE = 2.4 cm, find the length of BC.
- BC = 4.8 cm, find the length of DE.
In the given figure, PQ || AB; CQ = 4.8 cm QB = 3.6 cm and AB = 6.3 cm. Find : PQ
In ΔABC, D and E are the points on sides AB and AC respectively. Find whether DE || BC, if AB = 6.3 cm, EC = 11.0 cm, AD = 0.8 cm and AE = 1.6 cm.
Find the area of the triangle ABC with the coordinates of A as (1, −4) and the coordinates of the mid-points of sides AB and AC respectively are (2, −1) and (0, −1).
The model of a building is constructed with scale factor 1:30.
(i) If the height of the model is 80 cm, find the actual height of the building in metres.
(ii) If the actual volume of a tank at the top of the building is 27 m3, find the volume of the tank on the top of the model.
If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:
AB = 5.6cm, AD = 1.4cm, AC = 7.2cm, and AE = 1.8cm
In ΔABC, point D divides AB in the ratio 5:7, Find: BC, If DE = 2.5cm
A plot of land of area 20km2 is represented on the map with a scale factor of 1:200000. Find: The number of KM represented by 2cm on the map.
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
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`
In the given figure, if ΔEAT ~ ΔBUN, find the measure of all angles.
If ΔABC ~ ΔLMN and ∠A = 60° then ∠L = ?
ΔABC ~ ΔPQR, A(ΔABC) = 80 sq.cm, A(ΔPQR) = 125 sq.cm, then complete `("A"(Δ"ABC"))/("A"(Δ"PQR")) = 80/125 = (["______"])/(["______"])`, hence `"AB"/"PQ" = (["______"])/(["______"])`
