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Question

Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle


A

3cm,4cm,6cm

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B

9cm,16cm,26cm

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C

1.5cm,3.6cm,3.9cm

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D

7cm,24cm,26cm

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Solution

The correct option is C

1.5cm,3.6cm,3.9cm


Explanation for the correct options:

Option (C): 1.5cm,3.6cm,3.9cm

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse,c is equal to the sum of the squares of the other two sides a,b.

i.e. c2=a2+b2

Consider, 1.5cm,3.6cm,3.9cm compare the value with values a,b, and c:

a=1.5,b=3.6,c=3.9

Apply value into the above-given formula:

3.92=1.52+3.6215.21=2.25+12.9615.21=15.21

Hence, option C is correct .

Option (A): 3cm,4cm,6cm

Consider, 3cm,4cm,6cm compare the value with values a,b, and c:

a=3,b=4,c=6

Apply value into the above-given formula:

62=32+4236=9+163625

Hence, option A is in-correct .

Option (B): 9cm,16cm,26cm

Consider 9cm,16cm,26cmcomparing the value with values a,b, and c:

a=9,b=16,c=26

Apply value into the above-given formula:

262=92+162676=81+256676337

Hence, option B is in-correct .

Option (D): 7cm,24cm,26cm

Consider, 7cm,24cm,26cm compare the value with values a,b, and c:

a=7,b=24,c=26

Apply value into the above-given formula:

262=72+242676=49+576676625

Hence, option D is in-correct .

Hence, the correct choice is option C.


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