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.#

2 Answers
Feb 22, 2018

#"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"#

Feb 22, 2018

#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#