Question

Try to construct triangles using match sticks. Some are shown here. Can you make a triangle with: (a) 3matchsticks? (b) 4matchsticks? (c) 5matchsticks? (d) 6matchsticks? (Remember you have to use all the available matchsticks in eachcase). If you cannot make a triangle, think of reasons forit.

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Answer 1

$\maltese$ $\bold{\red{\underline{SOLUTION :}}}$ $\maltese$

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(a) 3 matchsticks

1st side=1 matchsticks

2nd side = 1 matchsticks

3rd side=1 matchsticks.

Hence, it forms an equilateral triangle.

(b) 4 matchsticks

1st side=1 matchsticks

2nd side = 1 matchsticks

3rd side=2 matchsticks.

If we make triangle with 4 matchsticks, then it should obey the rule, where the sum of two sides of a triangle is greater than the third side. But this rule is not applicable here since if we add 1 + 1 (matchsticks), it is equal to 2, which is the length of the third side of the triangle. Hence, we can make a triangle with 4 matchsticks.

(c) 5 matchsticks

1st side=2 matchsticks

2nd side = 2 matchsticks

3rd side=1 matchsticks.

Hence, it forms an isosceles triangle.

(d) 6 matchsticks

1st side=2 matchsticks

2nd side = 2 matchsticks

3rd side=2 matchsticks.

Hence, it forms an equilateral triangle.

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