Advertisements
Advertisements
प्रश्न
Given `triangle ABC ~ triangle PQR`, if `(AB)/(PQ) = 1/3`, then find `(ar triangle ABC)/(ar triangle PQR)`
उत्तर १
`(A(triangle ABC))/(A(triangle PQR)) = (AB)^2/(PQ)^2`
(Ratio of area of the similar triangle is equal to the square of their proportional sides)
`(A(triangle ABC))/(A(triangle PQR)) = (1/3)^2 = 1/9`
उत्तर २
Given `triangle ABC ~ triangle PQR`
Also `(AB)/(PQ) = 1/3`
We know if two triangles are similar then the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides
`(ar triangle ABC)/(ar triangle PQR) = ((AB)/(PQ))^2 = (1/3)^2 = 1/9`
APPEARS IN
संबंधित प्रश्न
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.
State, true or false:
All equiangular triangles are similar.
In triangle ABC, AD is perpendicular to side BC and AD2 = BD × DC. Show that angle BAC = 90°.
Area of two similar triangles are 98 sq. cm and 128 sq. cm. Find the ratio between the lengths of their corresponding sides.
The given diagram shows two isosceles triangles which are similar. In the given diagram, PQ and BC are not parallel; PC = 4, AQ = 3, QB = 12, BC = 15 and AP = PQ.
Calculate:
- the length of AP,
- the ratio of the areas of triangle APQ and triangle ABC.
In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.
In ∆ABC, AP ⊥ BC, BQ ⊥ AC B– P–C, A–Q – C then prove that, ∆CPA ~ ∆CQB. If AP = 7, BQ = 8, BC = 12 then Find AC.
O is any point in the interior of ΔABC. Bisectors of ∠AOB, ∠BOC and ∠AOC intersect side AB, side BC, side AC in
F, D and E respectively.
Prove that
BF × AE × CD = AF × CE × BD
Δ ABC ∼ Δ PQR such that AB= 1.5 cm and PQ=2. 1 cm. Find the ratio of areas of Δ ABC and ΔPQR.
A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A' B' C'. Calculate : the length of C' A' if CA = 4 cm.
A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find : OA, if OA' = 6 cm.
In the following figure, M is mid-point of BC of a parallelogram ABCD. DM intersects the diagonal AC at P and AB produced at E. Prove that : PE = 2 PD
In fig.DE || BC ,AD = 1 cm and BD = 2 cm. what is the ratio of the ar(ΔABC) to the ar (ΔADE)?
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 the given figure, AB and DE are perpendicular to BC.
- Prove that ΔABC ∼ ΔDEC
- If AB = 6 cm, DE = 4 cm and AC = 15 cm. Calculate CD.
- Find the ratio of the area of a ΔABC : area of ΔDEC.
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD : BD = 4 : 5 and EC = 2.5cm, find AE.
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 figure, PQ is parallel to BC, AP : AB = 2 : 7. If QC = 0 and BC = 21,
Find
(i) AQ
(ii) PQ
Given is a triangle with sides 3 cm, 5 cm and 6 cm. Find the sides of a triangle which is similar to the given triangle and its shortest side is 4.5 cm.
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.
If figure OPRQ is a square and ∠MLN = 90°. Prove that ∆LOP ~ ∆QMO
If ∆ABC is an isosceles triangle with ∠C = 90° and AC = 5 cm, then AB is
In any triangle _______ sides are opposite to equal angles
State whether the following triangles are similar or not: If yes, then write the test of similarity.
∠P = 35°, ∠X = 35° and ∠Q = 60°, ∠Y = 60°
In ΔABC, AP ⊥ BC and BQ ⊥ AC, B−P−C, A−Q−C, then show that ΔCPA ~ ΔCQB. If AP = 7, BQ = 8, BC = 12, then AC = ?
In ΔCPA and ΔCQB
∠CPA ≅ [∠ ______] ...[each 90°]
∠ACP ≅ [∠ ______] ...[common angle]
ΔCPA ~ ΔCQB ......[______ similarity test]
`"AP"/"BQ" = (["______"])/"BC"` .......[corresponding sides of similar triangles]
`7/8 = (["______"])/12`
AC × [______] = 7 × 12
AC = 10.5
ΔABC and ΔBDE are two equilateral triangles such that D is the mid point of BC. Ratio of the areas of triangle ΔABC and ΔBDE is ______.
In the given figure the value of x is
In ∠BAC = 90° and AD ⊥ BC. A then ______.
In the given figure, ∠ACB = ∠CDA, AC = 8cm, AD = 3cm, then BD is ______.
In figure, if AD = 6 cm, DB = 9 cm, AE = 8 cm and EC = 12 cm and ∠ADE = 48°. Find ∠ABC.
