Practice30Create account

A triangle has 3 medians and 3 altitudes — six segments in all. In an obtuse-angled triangle, how many of these six lie completely inside the triangle?

Class 7The Triangle and its PropertiesTriangles
  • A6
  • B3
  • C4
  • D5

Step-by-Step Solution

All 3 medians lie inside every triangle, because each one ends at the midpoint of a side. Of the altitudes, only the one drawn from the obtuse vertex lands on the opposite side; the other two fall outside, on extensions of the sides. So 3 + 1 = 4 lie completely inside. Trap: assuming altitudes behave like medians and answering 6.
Answer: C) 4

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 ABC, angle B = 90°. A point D lies on BC and AD is joined, with angle BAD =…In triangle PQR, angle P = 40°. The remaining two angles, angle Q and angle R, are in…Rohit tests whether 5 cm, 9 cm and 14 cm can be the sides of a triangle. He writes "9 +…Which set of lengths CANNOT be the sides of a triangle?In triangle XYZ, XY = XZ and angle X = 104°. Which side is the longest?