Question

Check whether 2 cm, 3 cm, 4 cm can be the sides of a right–angled triangle or not. Name the property used​

Answer 1

Given -

• Measure of right - triangle = 2cm, 3cm, and 4cm

To find -

• To find whether the above measure can be the sides of right-angled triangle.

Solution -

Let -

2cm = A

3cm = B

4cm = C

Now ,

Here the 4cm is the longest measure, therefore, it will be termed as hypotenuse. Now, we will apply Pythagoras theorem.

(Hypotenuse)² = (Measure A)² + (Measure B)²

On substituting the values -

$\longmapsto$ (4cm)² = (2cm)² + (3cm)²

$\longmapsto$ 16cm = 4cm + 9cm

$\longmapsto$ 16cm ≠ 13cm

$\therefore$ The above measures cannot be the sides of the right-angled triangle.

Property used -

$\longmapsto$ Pythagoras theorem.

Learn more !!

What is the Pythagoras theorem ?

$\longmapsto$ Pythagoras theorem is the theorem used to tell the area of the right-angled triangle by squaring the hypotenuse and the sides given, and checking whether the square of hypotenuse is equal to the sum of square of the two sides.

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Answer 2

$\bf{\blue{Given-}}$

• Measure of right triangle = 2cm, 3cm and 4cm

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$\bf{\blue{To\: find-}}$

• whether the given measures can be the sides of right angle triangle.

• property used.

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$\bf{\blue{Let-}}$

• 2cm = A
• 3cm = B
• 4cm = C

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$\bf{\blue{Solution-}}$

Now,

In the given measures 4cm is the longest measure. Hence it will be known as Hypotenuse.

Here lets use Pythagoras theorem;

( Hypotenuse)² = ( A )² + ( B )²

Substitute the given values ;

${ \bold {: \implies} }$ ( 4cm )² = ( 2cm )² + ( 3cm )²

${ \bold {: \implies} }$ 16cm = 4cm + 9cm

${ \bold {: \implies} }$ 16cm ≠ 13cm.

Hence it is proved that the given measures cannot be a right angled triangle.

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$\bf{\blue{Property\: used-}}$

$\boxed{ \fcolorbox{blue}{black}{ \boxed{\bold{ \blue{Pythagoras\: theorem.}}}}}$

$\bf{\blue{More\: information-}}$

• Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

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