7.
In which of the following cases is the construction of a triangle ABC
possible?
(b) AB = 5 cm, BC = 7 cm. CA = 8 cm
(a) AB = 3 cm, BC = 4 cm, CA = | cm
(C) AB = 9 cm, BC = 4 cm, CA = 3 cm
(d) AB = 10 cm, BC = 7 cm, CA = 8 cm
1
B
CONSTRUCTION with full explaining
Answers
Answer:
b) and d)
Step-by-step explanation:
(b) AB = 5 cm, BC = 7 cm. CA = 8 cm
The sum of the lengths of the smaller line segments = AB = 5 cm + BC = 7 cm
The length of the longest line segment = CA = 8 cm
Thus, the sum of the lengths of the two smaller line segments is greater than the length of the longest line segment.
Hence, the line segments AB = 5 cm, BC = 7 cm and CA = 8 cm can form a triangle.
(a) AB = 3 cm, BC = 4 cm, CA = | cm
The sum of the lengths of the smaller line segments = AB = 3 cm + CA = 1 cm
The length of the longest line segment = BC = 8 cm
Thus, the sum of the lengths of the two smaller line segments is not greater than the length of the longest line segment.
Hence, the line segments AB = 3 cm, BC = 4 cm and CA = | cm cannot form a triangle.
C) AB = 9 cm, BC = 4 cm, CA = 3 cm
The sum of the lengths of the smaller line segments = BC = 7 cm + CA = 5 cm
The length of the longest line segment = AB = 9 cm
Thus, the sum of the lengths of the two smaller line segments is not greater than the length of the longest line segment.
Hence, the line segments AB = 5 cm, BC = 7 cm and CA = 8 cm cannot form a triangle.
(d) AB = 10 cm, BC = 7 cm, CA = 8 cm
The sum of the lengths of the smaller line segments = BC = 7 cm + CA = 8 cm
The length of the longest line segment = AB = 10 cm
Thus, the sum of the lengths of the two smaller line segments is greater than the length of the longest line segment.
Hence, the line segments AB = 10 cm, BC = 7 cm and CA = 8 cm can form a triangle.
Answer:
Step-by-step explanation: