Question

Which of the following ratios do not match with the sides of a triangle?
(Select two correct alternative)
(1) 2:3:4
(2) 1:2:3
(3) 4:5:7
(4) 2:3:5​

Answer 1

$\sf\huge\bold{Solution}$

(2) and (4) Ratios do not match with sides of triangle.

Given

Ratios of sides

(1)2:3:4

(2)1:2:3

(3)4:5:7

(4)2:3:5

To find

which ratios satisfies the sides of triangle

Triangle's Inequality Theorem

This theorem states that the sum of any two sides of triangle must be equal to the third side.

Now,checking one by one all ratios of sides

(1)2:3:4

2+3=5

∵5>4 [sum of any two sides is greater than the third one ] so,this ratios are the sides of triangle.

(2)1:2:3

1+2=3

3=3[Here,sum of two sides is equal to the third side which doesn't satisfy the triangle theorem of inequality ]so,this ratios are not the sides of triangle.

(3)4:5:7

4+5=9

∵9>7[Sum of two sides is greater than the third side say 7]so,this ratios are the sides of triangle.

(4)2:3:5

2+3=5

∵5=5[Here,sum of two sides is equal to the third side which not satisfy the triangle Theorem of inequality]So,this ratios are not the sides of triangle.