Question

In which case of the following lengths of sides of a triangle, is it possible to draw a triangle? (а) 3 cm, 4 cm, 7 cm (b) 2 cm, 3 cm, 7 cm (c) 3 cm, 4 cm, 5 cm​

Answer 1

Answer:

the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

3 + 4 > 5; 4 + 5 > 3; 5 + 3 > 4.

so option c is correct

mrk me as brainliest plzzzz

Answer 2

Solution :-

We know that, In any ∆ we have,

• Sum of any two sides of a ∆ is always greater than the third side .
• Difference between any two sides of a ∆ is always smaller than the third side .

So, checking all given options we get,

(а) 3 cm, 4 cm, 7 cm

→ 3 + 4 < 7 => 7 = 7

also,

→ 7 - 3 > 4 => 4 = 4

since sum of first two sides is not greater than third side and difference between third and first side is not smaller than second side but it is equal to third side . Therefore, triangle with sides is not possible .

(b) 2 cm, 3 cm, 7 cm

→ 2 + 3 > 7 => 5 < 7

also,

→ 7 - 2 < 3 => 5 > 3

since sum of first two sides is not greater than third side and difference between third and first side is not smaller than second side . Therefore, triangle with sides is not possible .

(c) 3 cm, 4 cm, 5 cm

→ 3 + 4 > 5 => 7 > 5

→ 4 + 5 > 3 => 9 > 3

→ 3 + 5 > 4 => 8 > 4

and,

→ 4 - 3 < 5 => 1 < 5

→ 5 - 4 < 3 => 1 < 3

→ 5 - 3 < 4 => 2 < 4

therefore, the given sides are possible .

Hence, we can conclude that, Option (c) can be the sides of a triangle .

Learn more :-

two sides of a triangle are of length 4 cm and 2.5 CM the length of the third side of the triangle cannot be

a). 6cm

b)....

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