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Let ABC be a right angled triangle with AC as its hypotenuse. Then,

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Let ABC be a right angled triangle with AC as its hypotenuse. Then,

(a) AC3 > AB3 + AC3 

(b) AC2 > AB2 + BC2 

(c) AC > AB + BC 

(d) None of these

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(a) AC3 > AB3 + AC3 

In a right angled triangle, hypotenuse is the longest side, so in ΔABC, AC > BC and AC > AB 

AC3 = AC2 · AC 

= (AB2 + BC2) · AC 

= AB2 · AC + BC2 · AC > AB2 · AB + BC2 · BC 

∴ AC > BC, AC > AB

⇒ AC3 > AB3 + BC3.

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