Justify with reasons:
i) Line Segments of length 10cm, 2cm, and 12 cm can't form a triangle.ii) Line Segments of 9cm, 10cm, and 11cm can form a right triangle.

(i) In a triangle, the sum of any two sides should be greater than the third side.

Therefore,

10 cm + 2 cm = 12 cm is equal to the third side 12 cm.

Therefore, line segments of length 10 cm, 2 cm and 12 cm cannot form a triangle.

(ii) In a right-angled triangle, the sum of the squares of two sides is equal to the square of the hypotenuse.

Given line segments are 9 cm, 10 cm and 11 cm.

$(9)^2+(10)^2=81+100=181$

$(11)^2=121$

Here, sum of the squares of two sides is not equal to the square of the third (largest) side.

Therefore, line segments of length 9 cm, 10 cm and 11 cm cannot form a right-angled triangle.

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Updated on: 10-Oct-2022

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