Rosa wants to make a triangle using three rods. The lengths of the rods are 5 cm, 7, cm and 7 cm. Which statement is true?
no statements, but it sure looks like an isosceles triangle with base=5.
To determine if Rosa can make a triangle using the given rods, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check if this condition is met for the given rods:
1. Sum of the lengths of the first two rods:
5 cm + 7 cm = 12 cm
Is the sum greater than the length of the third side (7 cm)?
Yes, 12 cm is greater than 7 cm.
2. Sum of the lengths of the first and third rods:
5 cm + 7 cm = 12 cm
Is the sum greater than the length of the second side (7 cm)?
Yes, 12 cm is greater than 7 cm.
3. Sum of the lengths of the second and third rods:
7 cm + 7 cm = 14 cm
Is the sum greater than the length of the first side (5 cm)?
Yes, 14 cm is greater than 5 cm.
Since the sum of the lengths of any two sides is greater than the length of the third side for all three combinations, Rosa can make a triangle using the given rods.
Therefore, the statement "Rosa can make a triangle using the rods with lengths 5 cm, 7 cm, and 7 cm" is true.
To determine whether Rosa can make a triangle using three rods, we need to check if the sum of the lengths of any two rods is greater than the length of the third rod. Let's go through each possible combination:
1. Rod 1 (5 cm) + Rod 2 (7 cm) = 12 cm. This is greater than the length of Rod 3 (7 cm). Thus, Rods 1 and 2 can form a triangle with Rod 3.
2. Rod 1 (5 cm) + Rod 3 (7 cm) = 12 cm. Again, this is greater than the length of Rod 2 (7 cm). Therefore, Rods 1 and 3 can form a triangle with Rod 2.
3. Rod 2 (7 cm) + Rod 3 (7 cm) = 14 cm. This is equal to the length of Rod 1 (5 cm). Hence, Rods 2 and 3 can form a triangle with Rod 1.
Based on the analysis, it can be concluded that all three rods can form a triangle.