Practice30Create account

Which set of lengths CANNOT be the sides of a triangle?

Class 7The Triangle and its PropertiesTriangles
  • A7 cm, 7 cm, 13 cm
  • B9 cm, 10 cm, 18 cm
  • C6 cm, 11 cm, 15 cm
  • D7 cm, 7 cm, 15 cm

Step-by-Step Solution

Test the two shortest sides in each set. 7 + 7 = 14 > 13, 9 + 10 = 19 > 18 and 6 + 11 = 17 > 15 all pass, but 7 + 7 = 14, which is less than 15, fails. Trap: the first and last options differ only in the largest side, and that is exactly the side that decides — eyeballing the two equal 7s proves nothing.
Answer: D) 7 cm, 7 cm, 15 cm

Key idea: Triangle inequality

**The sum of any two sides of a triangle is greater than the third side.**

So a triangle with sides 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3). But sides 1, 2, 5 do NOT form a triangle — 1 + 2 = 3 is less than 5, so the two short sides can't reach across.

Use this to test whether three given lengths can be a triangle, or to bound a missing side: if two sides are 5 and 8, the third must be greater than 8 − 5 = 3 AND less than 8 + 5 = 13.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All The Triangle and its Properties practice questions

More Class 7 The Triangle and its Properties practice

In triangle XYZ, XY = XZ and angle X = 104°. Which side is the longest?In triangle DEF, DE = 8 cm, EF = 8 cm and DF = 5 cm. Which angle is the smallest?A right triangle has hypotenuse 26 cm and one leg 24 cm. Find the other leg in cm.Which of these is NOT a Pythagorean triple?A bamboo pole standing upright snaps at a point above the ground. The broken part stays…