Question

Which list shows the lengths of three line segments that could not form a triangle? `A. 6 cm, 8 cm, 10cm" " B. 5 cm, 6 cm, 7 cm" "C. 4 cm, 7 cm, 13 cm` `D. 3 cm, 6 cm, 6 cm.`

Answer 1

`"list "C`

Explanation:

`"for a triangle to be constructed we require that"`

`•" the sum of 2 sides ">" third side"`

`"consider list C with sides 4, 7 and 13"`

`4+13=17>7larr" valid"`

`7+13=20>4larr"valid"`

`4+7=11<13larr"not valid"`

`"this set could not form a triangle"`

Answer 2

`C` cannot form a triangle

Explanation:

`A` can form a right-triangle,proved by using Pythagoras' theorem
(`a^2 = b^2 + c^2`)
`10^2=8^2+6^2`. This means the triangle is right-angled.

`B` can form a triangle by using the cosine rule
(`a^2=b^2+c^2-2bc cos(A)`)
`7^2=5^2+6^2-2xx5xx6xxcos(A)`
`49=61-60xxcos(A)`
`-12=-60xxcos(A)`
`1/5=cos(A)`
`A=cos^-1(1/5)`
`A=78.46`
This gives an answer so the triangle can be formed.

`D` can form an isosceles triangle because two of the sides are the same length

`C` cannot form a triangle because it does not give an answer when you put the numbers into the cosine equation. After simplification, it gives:
`-13/7=cos(A)`
`cos^-1` is not possible with values more than `1`