Class 10, Maths, Chapter 6, Exercise 6.4 Solutions
Q.1. Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.
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Q.2. Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
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Q.3. In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that $\frac{ar\,\,(ABC)}{ar\,\,(DBC)}=\frac{AO}{DO}$
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Q.4. If the areas of two similar triangles are equal, prove that they are congruent.
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Q.5. D, E and F are respectively the mid-points of sides AB, BC and CA of Δ ABC. Find the ratio of the areas of Δ DEF and Δ ABC.
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Q.6. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
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Q.7. 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.
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Tick the correct answer and justify :
Q.8. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
(A) 2 : 1
(B) 1 : 2
(C) 4 : 1
(D) 1 : 4
Ans: (C) correct answer. (See below)
Q.9. Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles are in the ratio
(A) 2: 3
(B) 4 : 9
(C) 81 : 16
(D) 16 : 81
Ans: (D) is the correct answer.