A triangle has sides 10 cm, 12 cm and 15 cm. Is it right-angled?

Class 7The Triangle and its PropertiesTriangles

ANo — $1 0^{2} + 1 2^{2} = 244$ , which is not equal to $1 5^{2} = 225$ .
BYes — $1 0^{2} + 1 2^{2} = 1 5^{2}$ .
CYes — because 10 + 12 is greater than 15.
DNo — these three lengths cannot form a triangle at all.

Step-by-Step Solution

By the converse of Pythagoras, a triangle is right-angled only if the square of the longest side equals the sum of the squares of the other two. Here

1 0^{2} + 1 2^{2} = 100 + 144 = 244

while

1 5^{2} = 225

, so it is not right-angled. Trap: reading 10 + 12 > 15 as proof of a right angle — that is the triangle inequality, and it only shows the triangle EXISTS, which it does.

Answer: A) No —

1 0^{2} + 1 2^{2} = 244

, which is not equal to

1 5^{2} = 225

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

Two sides of a triangle measure 7 cm and 11 cm. Between which two values must its…Side BC of triangle ABC is extended to D. If ∠A = 45° and ∠B = 70°, find the exterior…In triangle ABC the tick marks show AB = AC, and ∠A = 40°. Find the angle x at C.Two segments are drawn from A to side BC: the dashed segment AD, which has a right-angle…Ravi has four sticks of lengths 3 cm, 5 cm, 7 cm and 9 cm, drawn to scale. He picks any…