Ratio of Area of Similar Triangles
Trending Questions
P and Q are points on the sides AB and AC respectively of △ABC such that PQ||BC and divides △ABC into two parts, equal in area. Find PB : AB.
- 3:4
- 4:3
- 9:16
- 16:9
In the given figure, △ABC and △DEF are similar. If BC = 3 cm, EF = 4 cm and area of △ABC is 54 cm2, then the area of △DEF is _____ cm2.
- 96
- 48
- 24
- 64
The areas of two similar triangles are 9 cm2 and 16 cm2 respectively . The ratio of their corresponding sides is ____.
3: 4
4: 3
4: 5
2: 3
Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of corresponding heights is :
5: 4
3: 2
5: 7
4: 5
The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller one is 2.1 cm, then the corresponding height of the larger one is
4.2 cm
4.41 cm
8.4 cm
0.525 cm
- 1 : 5
- 2 : 5
- 2 : 3
- 1 : 4
In an equilateral triangle, prove that the centroid and the centre of the circumcircle (circumcentre) coincide. [4 MARKS]
ABCD is a square. Equilateral triangles ACF and ABE are drawn on the the diagonal AC and side AB respectively. Find area of △ACF : area of △ABE.
4:1
√2:1
8:1
2:1
O is any point inside a triangle ABC. The bisector of ∠AOB, ∠BOC and ∠COA meet the sides AB. BC and CA in point D. E and F respectively. Show that AD × BE × CF = DB × EC × FA. [4 MARKS]
In the given figure, ABC is a triangle. DE is parallel to BC and ADDB=32. If the area of ΔDEF is 81cm2. The area of ΔCFB is
180 cm2
250 cm2
225 cm2
195 cm2
[2 Marks]
AM and PN are the medians of two similar triangles, △ABC and △PQR respectively and Area of △ABCArea of △PQR = 925.
If AM = PO = 5 cm, find the value of 3 ON.
- 10 cm
- 12 cm
- 13 cm
- 9 cm
- 1√2
- (√3−1)√3
- (√2−1)√2
- (√3−1)√2
- 1 : 9
- 3 : 1
- 1 : 3
- 9 : 1
Question 3
Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.
- 1:1
- (√2−1):1
- (√2−1):√2
- 1:√2
- 13 : 45
- 14 : 93
- 25 : 144
- 1 : 5
If D, E, F are respectively the mid-points of the sides BC, CA, and AB of △ABC, and the area of △ ABC is 24 cm2, then find the area of △ DEF.
12 cm2
8 cm2
24 cm2
6 cm2
In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2 , then the area of △ DEF
- 96cm2
- 96m2
- 9.6m2
- 96cm2
△ABC is such that AB=3 cm, BC=2 cm and CA=2.5 cm. △DEF is similar to △ABC. If EF=4 cm, then the perimeter of △DEF is ____.
7.5 cm
15 cm
22.5 cm
30 cm
- 180 cm2
- 250 cm2
- 225 cm2
- 195 cm2
E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF || QR.
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
- 180 cm2
- 250 cm2
- 225 cm2
- 195 cm2
The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller triangle is 2.1 cm, then the corresponding height of the bigger triangle is _____.
4.41 cm
8.4 cm
4.2 cm
0.525 cm
In given figure △ ABC and △ DEF are similar, EF=3cm, BC=4cm, and area of triangle DEF=54cm2 . Find the area of △ ABC.
In figure, if DEIIBC, find the ratio of ar (ΔADE) and ar (ΔDECB).
△ABC and △PQR are two similar triangles as shown in the figure such that Area of ABCArea of PQR = 925. AM and PN are the medians on △ABC and △PQR respectively. If AM = PO = 5 cm, find the value of 3ON.
- 180 cm2
- 250 cm2
- 225 cm2
- 195 cm2