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Standard VIII

Mathematics

Quadrilateral

Which of the ...

Question

Which of the following can be the sides of a triangle?
(i) 1, 2, 4 (ii) 3, 6, 8

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Solution

(i) Here 1 + 2 = 3 = the measure of third side.
In a triangle the sum of the measures of any two sides must be greater than the third side. $[1]$

∴ 1,2,4 cannot be the sides of a triangle.

(ii) Here 3 + 6 = 9 = the measure of third side.
In a triangle the sum of the measures of any two sides must be greater than the third side. $[1]$

∴ 3,6,8 can be the sides of a triangle.

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Similar questions

Two sides of a triangle are 6-4 m and 4-8 m. If height of the triangle corresponding to 4-8 m side id 6 m; find:

(i) Area of the triangle;

(ii) Height of the triangle corresponding to 6-4 m side

Suppose we want to draw a triangle with one side 6 centimeters long. Which of the following pairs of lengths can be the lengths of the other two sides?

(i) 4 cm, 1 cm

(ii) 4 cm, 2 cm

(iii) 4 cm, 3 cm

(iv) 5 cm, 10 cm

(v) 5 cm, 11 cm

(vi) 5 cm, 12 cm

Q. Find area of triangle with vertices at the point given in each of the following
(i)

(1, 0), (6, 0), (4, 3)

(ii)

(2, 7), (1, 1), (10, 8)

(iii)

(- 2, - 3), (3, 2), (- 1, - 8)

Q. Verify the following
(i)

(0, 7, - 10), (1, 6, - 6)

and

(4, 9, - 6)

are the vertices of an isosceles triangle
(ii)

(0, 7, 10), (- 1, 6, 6)

and

(- 4, 9, 6)

are the vertices of a right angled triangle
(iii)

(- 1, 2, 1), (1, - 2, 5), (4, - 7, 8)

and

(2, - 3, 4)

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Two sides of a triangle are 6 cm and 8 cm. If height of the triangle corresponding to 6 cm side is 4 cm; find:

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Which of the following can be the sides of a triangle? (i) 1, 2, 4 (ii) 3, 6, 8

Which of the following can be the sides of a triangle?
(i) 1, 2, 4 (ii) 3, 6, 8