NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4.
- Triangles Class 10 Ex 6.1
- Triangles Class 10 Ex 6.2
- Triangles Class 10 Ex 6.3
- Triangles Class 10 Ex 6.4
- Triangles Class 10 Ex 6.5
- Triangles Class 10 Ex 6.6
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 10 |
| Subject | Maths |
| Chapter | Chapter 6 |
| Chapter Name | Triangles |
| Exercise | Ex 6.4 |
| Number of Questions Solved | 8 |
| Category | NCERT Solutions |
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4
Ex 6.4 Class 10 Maths Question 1.
Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.
Solution:
We have ∆ABC ~ ∆DEF
Ex 6.4 Class 10 Maths Question 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.
Solution:
In the figure below, a trapezium ABCD is shown, in which AB || DC and AB = 2DC. Its diagonals interest each other at the point O.
Ex 6.4 Class 10 Maths Question 3.
In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that: \(\frac { ar\left( ABC \right) }{ ar\left( DBC \right) } =\frac { AO }{ DO } \)
Solution:
Ex 6.4 Class 10 Maths Question 4.
If the areas of two similar triangles are equal, prove that they are congruent.
Solution:
Ex 6.4 Class 10 Maths Question 5.
D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ABC. Find the ratio of the areas of ∆DEF and ∆ABC.
Solution:
Ex 6.4 Class 10 Maths Question 6.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Solution:
Ex 6.4 Class 10 Maths Question 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.
Solution:
Ex 6.4 Class 10 Maths Question 8.
Tick the correct answer and justify
(i) 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
(ii) 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
Solution:
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