Question

The lengths of the sides of some triangles are given. Say what types of triangles they are.
(1) 3 cm, 4 cm, 5 cm
(2) 3.4 cm, 3.4 cm, 5 cm
(3) 4.3 cm, 4.3 cm, 4.3 cm
(4) 3.7 cm, 3.4 cm, 4 cm

Answer 1

1)scalene triangle
2)isosceles triangle
3)equilateral triangle
4)isosceles triangle

Answer 2

Answer:

(1): Right angled triangle.

(2): Isosceles triangle.

(3): Equilateral triangle.

(4): Scalene triangle.

Step-by-step explanation:

A triangle is called equilateral triangle if all of its three sides are equal to one another.

A triangle is called isosceles triangle if two of its sides are equal.

A triangle is called scalene triangle if none of its three sides are equal.

A triangle is called right-angled triangle if two of its sides make a right angle at the vertex of the triangle and its two sides make the right angle when it follows Pythagoras theorem which states,

$\rm (H)^2=(P)^2+(B)^2$

where,

• $\rm H$ = length of the hypotenuse of the triangle.

• $\rm P$ = length of the perpendicular of the triangle.

• $\rm B$ = length of the base of the triangle.

Now coming to question,

(1) 3 cm, 4 cm, 5, cm

Let's check for

$\rm H=5\ cm\\P=4\ cm,\\B=3\ cm\\\\H^2=5^2=25\ cm^2\\P^2=4^2=16\ cm^2\\B^2=3^2=9\ cm^2\\P^2+B^2=16+9=25\ cm^2 = H^2$

Therefore, it is a right angled triangle.

(2) 3.4 cm, 3.4 cm, 5 cm

Two of the sides of the triangle are equal therefore it is a isosceles triangle.

(3) 4.3 cm, 4.3 cm, 4.3 cm

All the three sides of the triangle are equal therefore it is an equilateral triangle.

(4) 3.7 cm, 3.4 cm, 4 cm

None of the sides of the triangle are equal and it also does not follow Pythagoras theorem, therefore it is a scalene triangle.