Question

Which of the side lengths could form a triangle? A) 2 cm, 2 cm, 4 cm B) 3 cm, 5 cm, 10 cm C) 3 cm, 4 cm, 5 cm D) 4 cm, 8 cm, 15 cm Eliminate

Answer 1

Option C.

Explanation:

To form a triangle we should always remember that a triangle is possible when sum of two smaller sides of the triangle is greater than the largest side.

If smaller sides are a, b and largest side is c

Then a + b > c

Now we take each option given

Option A) 2 cm, 2 cm, 4 cm

2 + 2 = 4 which equal to the largest side so to form a triangle is not possible.

Option B) 3 cm, 5 cm, 10 cm

3 + 5 = 8 < 10 cm

Here sum of smaller sides is less than to the largest side so triangle will not be formed.

Option C. 3 cm, 4 cm, 5 cm

3 + 4 = 7 > 5 cm

Therefore triangle can be formed.

Option D) 4 cm, 8 cm, 15 cm

4 + 8 = 12 < 15 cm

so triangle can not be formed.

Option C is the correct option.

Answer 2

Answer: The correct option is (C) 3 cm, 4 cm, 5 cm.

Step-by-step explanation: We are given to select the correct side lengths that could form a triangle.

We know that

the sum of the lengths of any two sides of a triangle is always greater than the third side.

That is, if a, b and c represents the lengths of three sides of a triangle, then we must have

`a+b>c,~~b+c>a,~~c+a>b.`

Option (A) is

a = 2 cm, b = 2 cm, c = 4 cm.

We have

`a+b=2+2=4=c~~~\Rightarrow a+b=c.`

Hence, this option is NOT correct.

Option (B) is

a = 3 cm, b = 5 cm, c = 10 cm.

We have

`a+b=3+5=8<10=c~~~\Rightarrow a+b<c.`

So, this option is NOT correct.

Option (C) is

a = 3 cm, b = 4 cm, c = 5 cm.

We have

`a+b=3+4=7>5=c~~~\Rightarrow a+b>c,\\\\b+c=4+5=9>3=a~~~\Rightarrow b+c>a,\\\\c+a=5+3=8>4=b~~~\Rightarrow c+a>b.`

So, this option is CORRECT.

Option (D) is

a = 4 cm, b = 8 cm, c = 15 cm.

We have

`a+b=4+8=12<15=c~~~\Rightarrow a+b<c.`

So, this option is NOT correct.

Thus, (C) is the correct option.