Select all the conditions for which it is possible to construct a triangle. A. A triangle with angle measures 60∘ , 80∘ , and 80∘ B. A triangle with side lengths 4 cm, 5 cm, and 6 cm C. A triangle with side lengths 4 cm, 5 cm, and 15 cm D. A triangle with side lengths 4 cm and 5 cm and a 50∘ angle E. A triangle with angle measures 30∘ and 60∘ , and a 3 cm side length
Answers
C. A triangle with side lengths 4 cm, 5 cm, and 15 cm
Select all the conditions for which it is possible to construct a triangle.
Question A) :- A triangle with angle measures 60∘ , 80∘ , and 80° . ?
Answer :-
→ sum of. all given angles = 60° + 80° + 80 = 220°
we know that, by angle sum property , sum of all three angles of a triangle is equal to 180°.
Therefore, it is not possible to construct the triangle.
Question B) :- A triangle with side lengths 4 cm, 5 cm, and 6 cm ?
Answer :-
As we know that, sum of any two sides of a triangle is greater than the third side and difference between two sides is less than third side .
So,
→ (4 + 5) > 6 , (5 + 6) > 4 , (4 + 6) > 5 .
→ (5 - 4) < 6, (6 - 5) < 4, (6 - 4) < 5.
Therefore, it is possible to construct the triangle.
Question C) A triangle with side lengths 4 cm, 5 cm, and 15 cm ?
Answer :-
As we know that, sum of any two sides of a triangle is greater than the third side and difference between two sides is less than third side .
So,
sum of two sides 4 and 5 is 9, which is not greater than 15cm.
Therefore, it is not possible to construct the triangle.
Question D) A triangle with side lengths 4 cm, 5 cm, and 50° angle ?
Answer :-
we have given two side length and one angle .
Therefore, it is possible to construct the triangle.
Question E :- A triangle with angle measures 30∘ and 60∘ , and a 3 cm side length.
Answer :-
we have given two angles and one side length .
Therefore, it is possible to construct the triangle.
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