A triangle can be constructed by taking its sides as
(1) 1.8 cm, 2.6 cm, 4.4 cm
(2) 2 cm, 3 cm, 4 cm
(3) 3.2 cm, 2.3 cm, 5.5 cm
(4) 2.4 cm, 2.4 cm, 6.4 cm
Answers
Answer:
(b) Triangle can be constructed only if they satisfy the given condition. Sum of two sides > Third side Clearly, only option (b) satisfies the given condition.
(2 + 3)cm > 4 cm i.e. 5 cm > 4 cm
Given,
(Four possible measures of an imaginary triangle)
(1) Side A of the triangle(A) = 1.8 cm
Side B of the triangle (B)= 2.6 cm
Longest Side C of the triangle (C)= 4.4 cm
(2) A=2 cm, B= 3cm and C= 4cm
(3) A= 3.2 cm, B= 2.3 cm and C= 5.5 cm
(4) A= 2.4, B=2.4 and C=6.4 cm
To find,
Whether a triangle can be constructed by taking its side as any of the above mentioned
Solution
We can solve this problem as given below:
Condition: In a triangle, the sum of two smaller sides will be greater than the longest side of the same triangle.
i.e.,
(A+B) > C
where A= Side A of the triangle, B= Side B of the triangle, and C= Longest Side C of the triangle.
Then,
(1) A+B= 1.8+2.6
= 4.4 cm
C = 4.4 cm
Here, "(A+B)=C", not "(A+B) > C"
Since the condition is not satisfied, a triangle cannot be constructed by taking its sides as 1.8 cm, 2.6 cm, and 4.4 cm.
(2) A+B= 2+3
= 5cm
C = 4cm
Here, "(A+B) > C".
Since the condition is satisfied, a triangle can be constructed by taking its sides as 2 cm, 3 cm, and 4 cm.
(3) A+B = 3.2+2.3
= 5.5 cm
C = 5.5 cm
Here, "(A+B)=C", not "(A+B) > C"
Since the condition is not satisfied, a triangle cannot be constructed by taking its sides as 3.2 cm, 2.3 cm, and 5.5 cm.
(4) A+B = 2.4+ 2.4
= 4.8 cm
C = 6.4 cm
Here, "(A+B) < C", not "(A+B) > C".
Since the sum of small sides of the triangle(A+B) is less than the longest side(C), a triangle cannot be constructed by taking its sides as 2.4 cm, 2.4 cm and 6.4 cm.
Thus, a triangle can be constructed by taking its sides as 2 cm, 3 cm, and 4 cm.