Class 7 Triangle Inequality — practice questions with answers
Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Complete the rule: in any triangle, the sum of the lengths of any two sides is ______ the length of the third side.
Aless than
Bgreater than
Chalf of
Dequal to
Show answer
Answer: B) greater than
Going straight from one corner to another is always shorter than going round through the third corner, so any two sides together are longer than the third side.
2. An isosceles triangle has two equal sides of 6 cm each. Which length can its base have?
A11 cm
B12 cm
C13 cm
D15 cm
Show answer
Answer: A) 11 cm
The base must be less than 6 + 6 = 12 cm. Only 11 cm works; 12 cm would make the sides lie flat.
3. ABCD is a quadrilateral with diagonals AC and BD. Which statement is true?
AAB + BC + CD + DA < AC + BD
BAB + BC + CD + DA > AC + BD
CAB + BC + CD + DA = AC + BD
DAC + BD > 2(AB + BC)
Show answer
Answer: B) AB + BC + CD + DA > AC + BD
Triangle ABC: AB + BC > AC. Triangle ACD: CD + DA > AC. Triangle ABD: AB + DA > BD. Triangle BCD: BC + CD > BD. Adding all four: 2(AB + BC + CD + DA) > 2(AC + BD).
4. Can a triangle have a perimeter of 20 cm with one side of 10 cm?
ANo, 10 cm is too short
BYes, any lengths will do
CYes, e.g. 5, 5, 10
DNo, the other two add to only 10 cm
Show answer
Answer: D) No, the other two add to only 10 cm
The other two sides add to 20 − 10 = 10 cm, which is not greater than 10 cm. So (5, 5, 10) and every other choice lie flat.
5. A triangle has whole-number sides. Two of them are 4 cm and 7 cm, and its perimeter is an even number. How many lengths are possible for the third side?
A7
B4
C2
D3
Show answer
Answer: D) 3
The third side c is more than 3 and less than 11: 4 to 10. Perimeter 11 + c is even only when c is odd: 5, 7, 9. So 3 lengths.