Question

2. Sandy made a reflective sticker for her bicycle in the shape of a triangle. Two of the three side lengths were 3 cm and 4 cm. (a) Could the third side of the reflective sticker be 6 cm long? Explain your reasoning. If this third side is possible, draw the triangle. (b) Could the third side of the reflective sticker be 1 cm long? Explain your reasoning. If this third side is possible, draw the triangle.

Answer 1

Answer:

(a) Triangle is possible

(b) Triangle is not possible

Step-by-step explanation:

Sandy made a reflective sticker for her in the shape of a triangle.

(a).Two of the three sides of the triangle are 3 cm and 4 cm.

we have to find whether triangle is possible or not if third side is 6 cm long.

By inequality theorem of the triangle

Sum of two sides of the triangle should be greater than the measure of third side.

So 3 + 4 = 7 > 6

4 + 6 = 10 > 3

6 + 3 = 9 > 4

Therefore, triangle is possible.

(b) If the third side of the triangle is 1 cm long then

3 + 1 = 4 (Third side should be greater than sum of rest two sides)

1 + 4 = 5 > 3

4 + 3 = 7 > 1

Therefore, triangle is not possible.

Answer 2

(a) The third side could be 6 cm long because the rule for this triangle is that the third side must be greater than 1 and less than 7. (4 - 3 = 1; 4 + 3 = 7) Then you can draw the triangle with Side 1 = 3 cm; Side 2 = 4 cm; Side 3 = 6 cm.

(b) The third side could not be 1 cm long because the rule for this triangle is that the third side must be greater than 1 and less than 7. (4 - 3 = 1; 4 + 3 = 7) This means that you cannot draw the triangle.