Question

A triangle has side lengths of 9 cm, 12 cm and 15 cm. The type of triangle is ...

A. scalene
B. right angled
C. equilateral
D. Isosceles​

Answer 1

A triangle has side lengths of 9 cm, 12 cm and 15 cm. The type of triangle is ...

A. scalene

B. right angled

C. equilateral

D. Isosceles

__________________________

Right angled triangle because 9cm, 12cm and 15cm are the Pythagorean triplets.

_______________________________

Answer 2

A triangle has side lengths of 9 cm, 12 cm and 15 cm. The type of triangle is a right triangle.

Discussion :

Determine the type of triangle :

If a triangle with lengths of sides a, b, and c is an oblique side, we can get the type of triangle as follows:

1. If c²> a² + b² => blunt triangle

2. If c² <a² + b² => acute triangle

3. If c² = a² + b² => right triangle

↓↓↓↓↓

Known :

Triangles with sides:

a = right side = 9 cm

b = right side = 12 cm

c = hypotenuse = 15 cm

Asked: Type of triangle?

Answer :

To determine which side is the hypotenuse, the hypotenuse is the longest side.

Therefore :

c² = a² + b²

15² = 9² + 12²

225 = 81 + 144

225 = 225✔️ => right triangle

So, the type of triangle with sides 15 cm, 12 cm, and 9 cm is a right triangle.