Question

b) Can 1.6 cm, 3.0 cm and 3.4 cm be the sides of right-angled triangle? solution yes or no ​

Answer 1

Answer :-

• Yes, 1.6 cm, 3.0 cm and 3.4 cm can be the sides of a right-angled triangle.

To find :-

• Whether 1.6 cm, 3.0 cm and 3.4 cm be the sides of a right angled triangle.

Step-by-step explanation :-

• We can find out whether the given sides can be of a right angled triangle or not by using the "Pythagoras theorem". If the Pythagoras theorem is satisfied, then the sides can be of a right angled triangle.

According to the Pythagoras theorem,

$\underline{\boxed{\sf Base^2 + Perpendicular^2 = Hypotenuse^2}}$

Let :-

• The base be 1.6 cm, perpendicular be 3.0 cm and the hypotenuse be 3.4 cm (as it's the longest side)

Applying the formula,

LHS

 

$\longrightarrow \: \sf{(1.6)}^{2} + {(3.0)}^{2}$

$\longrightarrow \: \sf{2.56 + 9}$

$\longrightarrow \: \sf{11.56 \: cm}$

RHS

$\longrightarrow \: \sf{(3.4)^2}$

$\longrightarrow \: \sf{11.56 \: cm}$

LHS = RHS.

The Pythagoras theorem is satisfied.

Hence :-

• The given sides can be of a right-angled triangle.