Advertisements
Advertisements
Question
If ∆ABC ~ ∆PQR and AB : PQ = 2 : 3, then fill in the blanks.
\[\frac{A\left( ∆ ABC \right)}{A\left( ∆ PQR \right)} = \frac{{AB}^2}{......} = \frac{2^2}{3^2} = \frac{......}{.......}\]
Solution
Given:
∆ABC ~ ∆PQR
AB : PQ = 2 : 3
According to theorem of areas of similar triangles "When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides".
\[\therefore \frac{A\left( ∆ ABC \right)}{A\left( ∆ PQR \right)} = \frac{{AB}^2}{{PQ}^2} = \frac{2^2}{3^2} = \frac{4}{9}\]
APPEARS IN
RELATED QUESTIONS
D, E, F are the mid-point of the sides BC, CA and AB respectively of a ∆ABC. Determine the ratio of the areas of ∆DEF and ∆ABC.
Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC
In Figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that `(ar(ABC))/(ar(DBC)) = (AO)/(DO)`
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals
The areas of two similar triangles are 25 cm2 and 36 cm2 respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.
In Figure, DE || BC If DE = 4 cm, BC = 6 cm and Area (ΔADE) = 16 cm2, find the area of ΔABC.
In Figure, DE || BC If DE = 4cm, BC = 8 cm and Area (ΔADE) = 25 cm2, find the area of ΔABC.
If ΔABC ~ ΔDEF such that AB = 5 cm, area (ΔABC) = 20 cm2 and area (ΔDEF) = 45 cm2, determine DE.
If D is a point on the side AB of ΔABC such that AD : DB = 3.2 and E is a Point on BC such that DE || AC. Find the ratio of areas of ΔABC and ΔBDE.
Areas of two similar triangles are 225 sq.cm. 81 sq.cm. If a side of the smaller triangle is 12 cm, then Find corresponding side of the bigger triangle.
The perpendicular from A on side BC of a Δ ABC meets BC at D such that DB = 3CD. Prove that 2AB2 = 2AC2 + BC2.
The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas.
In ΔABC, PQ is a line segment intersecting AB at P and AC at Q such that seg PQ || seg BC. If PQ divides ΔABC into two equal parts having equal areas, find `"BP"/"AB"`.
Ratio of areas of two similar triangles is 9 : 25. _______ is the ratio of their corresponding sides.
In the given figure DE || AC which of the following is true?
In a rectangle Length = 8 cm, Breadth = 6 cm. Then its diagonal = ______.
In the adjoining figure, ΔADB ∼ ΔBDC. Prove that BD2 = AD × DC.
Use area theorem of similar triangles to prove congruency of two similar triangles with equal areas.
If ΔABC ∼ ΔPQR and `(A(ΔABC))/(A(ΔPQR)) = 16/25`, then find AB : PQ.
