Which set of line segments can be used to construct a triangle? a) 2 cm, 8 cm, and 9 cm b) 3 cm, 6 cm, and 2 cm c) 5 cm, 9 cm, and 3 cm d) 6 cm, 3 cm, and 10 cm

option A is the correct answer

Step-by-step explanation:

The set of line segments that can be used is the one such that, its longest side is lesser than the semi perimeter,s[s=(a+b+c)/2] of the triangle.

If we apply this condition on the given line segments,

A) 2 cm, 8 cm, and 9 cm

s = (2+8+9)/2 = 9.5

9.5 is greater than 9cm

B) 3 cm, 6 cm, and 2 cm

s = (3+6+2)/2= 5.5

5.5 is lesser than 6. If we go on to look for the area using

Area = √s(s-a)(s-b)(s-c), it would be impossible because we would end up having square root of a negative number.

C) 5 cm, 9 cm, and 3 cm

s = (5+9+3)/2 = 8.5

8.5 is lesser than 9cm

If we go on to look for the area using

Area = √s(s-a)(s-b)(s-c), it would be impossible because we would end up having square root of a negative number.

D) 6 cm, 3 cm, and 10 cm

s = (6+3+10)/2 = 9.5

9.5 is lesser than 10

If we go on to look for the area using

Area = √s(s-a)(s-b)(s-c), it would be impossible because we would end up having square root of a negative number.

So option A is the correct answer

30

step-by-step explanation:

times by times

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6