Amir and Sofia are making a triangular sign for a community garden. Its three sides measure (4p + 3) cm, (7p − 2) cm and (5p + 1) cm, where p is a positive number. For each statement, write True, False or Not possible to tell.
- The perimeter of the sign is (16p + 4) cm.
- The side measuring (7p − 2) cm is longer than the side measuring (5p + 1) cm.
Need a hint?
For the second statement, try two different positive values of p that still allow the three lengths to form a triangle.
Worked answer
- (a) Perimeter = (4p + 3) + (7p − 2) + (5p + 1) = 16p + 2, not 16p + 4. So (a) is False.
- (b) Try p = 1: 7p − 2 = 5 and 5p + 1 = 6. The (7p − 2) cm side is shorter.
- Try p = 2: 7p − 2 = 12 and 5p + 1 = 11. The (7p − 2) cm side is longer.
- p could be either value, so (b) is Not possible to tell.
Answer: Not possible to tell
The mistake this question tests
Habit
Collecting like terms in algebra
Many pupils think the (7p − 2) cm side must be longer because 7p is more than 5p. When p is small the −2 and +1 matter: p = 1 gives 5 cm and 6 cm.
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