Question

identify which one is right angled triangle 11,12,15 or 11,,60,61
i want solution ​

Answer 1

Answer:

The biggest number among the given set is 61. Thus, (11, 60, 61) forms a Pythagorean triplet. Hence, the given triangle with sides 11, 60 and 61 is a right-angled triangle.

Step-by-step explanation:

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Answer 2

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Concept:

To identify which pair of length will be the sides of a right angled triangle, we put them in the Pythagoras theorem which is, (hypotenuse)$^2$ = (base)$^2$ + (height)$^2$. If, LHS = RHS, then that pair is a right angled triangle. The largest side is the hypotenuse and the others are base and height respectively.

Solution:

$1) 11, 12, 15 \\:\implies 15^2 = 11^2 + 12^2 \\:\implies 225 = 121 + 144 \\:\implies 225 = 265 \\\text{As LHS \neq RHS, this pair are not the sides of a right angled triangle}\\\\ 2) 11, 60, 61 \\:\implies 61^2 = 11^2 + 60^2 \\:\implies 3721 = 121 + 3600 \\:\implies 3721 = 3721 \\\text{As LHS=RHS, this pair are the sides of a right angled triangle}$

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