# 4.  Which of the following can be the sides of a right triangle?          (i) $\small 2.5\hspace{1mm} cm$, $\small 6.5\hspace{1mm} cm$, 6 cm.          (ii) 2 cm, 2 cm, 5 cm.         (iii) $\small 1.5\hspace{1mm} cm$, 2cm, $\small 2.5\hspace{1mm} cm$.          In the case of right-angled triangles, identify the right angles.

As we know,

In a Right-angled Triangle: By Pythagoras Theorem,

$(Hypotenus)^2=(Base)^2+(Perpendicular)^2$

(i) $\small 2.5\hspace{1mm} cm$, $\small 6.5\hspace{1mm} cm$, 6 cm.

As we know the hypotenuse is the longest side of the triangle, So

Hypotenuse = 6.5 cm

Verifying the Pythagoras theorem,

$(6.5)^2=(6)^2+(2.5)^2$

$42.25=36+6.25$

$42.25=42.25$

Hence it is a right-angled triangle.

The Right-angle lies on the opposite of the longest side (hypotenuse) So the right angle is at the place where 2.5 cm side and 6 cm side meet.

(ii) 2 cm, 2 cm, 5 cm.

As we know the hypotenuse is the longest side of the triangle, So

Hypotenuse = 5 cm

Verifying the Pythagoras theorem,

$(5)^2=(2)^2+(2)^2$

$25=4+4$

$25\neq8$

Hence it is Not a right-angled triangle.

(iii) $\small 1.5\hspace{1mm} cm$, 2cm, $\small 2.5\hspace{1mm} cm$.

As we know the hypotenuse is the longest side of the triangle, So

Hypotenuse = 2.5 cm

Verifying the Pythagoras theorem,

$(2.5)^2=(2)^2+(1.5)^2$

$6.25=4+2.25$

$6.25=6.25$

Hence it is a Right-angled triangle.

The right angle is the point where the base and perpendicular meet.

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