Question

Which of these can never be the ratio of the sides of the triangle? a. 3:5:7 b. 3:5:3 C. 2:2:3 d. 2:5:8​

Answer 1

Answer:

answer in attachment of only a hope help u

Answer 2

To Find :- Which of these can never be the ratio of the sides of the triangle ?

A) 3:5:7

B) 3:5:3

C) 2:2:3

D) 2:5:8

Concept used :-

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

Solution :-

Checking all given options we get,

A) 3 : 5 : 7

Let us assume that, sides of given ∆ are 3x , 5x and 7x unit .

So,

Sum of any two sides is greater than third side :-

→ 3x + 5x > 7x => 8x > 7x

→ 5x + 7x > 3x => 12x > 3x

→ 3x + 7x > 5x => 10x > 5x

Difference between any two sides is smaller than the third side :-

→ 5x - 3x < 7x => 2x < 7x

→ 7x - 5x < 3x => 2x < 3x

→ 7x - 3x < 5x => 4x < 5x

Therefore, given ratio is possible .

B) 3 : 5 : 3

Let us assume that, sides of given ∆ are 3x , 5x and 3x unit .

So,

Sum of any two sides is greater than third side :-

→ 3x + 5x > 3x => 8x > 3x

→ 5x + 3x > 3x => 8x > 3x

→ 3x + 3x > 5x => 6x > 5x

Difference between any two sides is smaller than the third side :-

→ 5x - 3x < 3x => 2x < 3x

→ 5x - 3x < 3x => 2x < 3x

→ 3x - 3x < 5x => 0 < 5x

Therefore, given ratio is possible .

C) 2 : 2 : 3

Let us assume that, sides of given ∆ are 2x , 2x and 3x unit .

So,

Sum of any two sides is greater than third side :-

→ 2x + 2x > 3x => 4x > 3x

→ 2x + 3x > 2x => 5x > 2x

→ 2x + 3x > 2x => 5x > 2x

Difference between any two sides is smaller than the third side :-

→ 2x - 2x < 3x => 0 < 3x

→ 3x - 2x < 2x => x < 2x

→ 3x - 2x < 2x => x < 2x

Therefore, given ratio is possible .

D) 2 : 5 : 8

Let us assume that, sides of given ∆ are 2x , 5x and 8x unit .

So,

Sum of any two sides is greater than third side :-

→ 2x + 5x > 8x

→ 7x > 8x

But, 8x > 7x .

Also,

Difference between any two sides is smaller than the third side :-

→ 8x - 2x < 5x

→ 6x < 5x

But, 6x > 5x .

Therefore, Sides of a ∆ can't be 2x , 5x and 8x units.

Hence, we can conclude that, Option (D) 2 : 5 : 8 can never be the ratio of the sides of the triangle .

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