Question

Which of the following can be a right triangle?
(i) $2.5cm,6.5cm,6cm$
(ii) $2cm,2cm,5cm$
(iii) $1.5cm,2cm,2.5cm$

Answer 1

Pythagoras theorem:

In a right angled triangle, the square of the hypotenuse is equal to sum of the squares of other two sides.

Here, the longest side is hypotenuse,

(i)

$2.5cm,6.5cm,6cm$

Longest side $=6.5cm$

${6.5}^2=42.25$

$(2.5{)}^2+6^2=6.25+36=42.25$

$\Rightarrow {6.5}^2=(2.5{)}^2+6^2$

By Pythagoras theorem, $2.5cm,6.5cm,6cm$ can form a right angled triangle.

(ii)

$2cm,2cm,5cm$

Longest side $=5cm$

$5^2=25$

$2^2+2^2=4+4=8$

$\Rightarrow 5^2\ne 2^2+2^2$

By Pythagoras theorem, $2cm,2cm,5cm$ cannot form a right angled triangle.

(iii)

$1.5cm,2cm,2.5cm$

Longest side $=2.5cm$

${2.5}^2=6.25$

${1.5}^2+2^2=2.25+4=6.25$

$\Rightarrow {2.5}^2={1.5}^2+2^2$

By Pythagoras theorem, $1.5cm,2cm,2.5cm$ can form a right angled triangle.