Question

Prove that in a triangle the hypotenuse is the greatest side then the other two sides ​

Answer 1

Answer:

Let's name triangle ABC

In triangel ABC

Angle Bb=90°

Angle B and Angle A,

$$AC>BC$$..................(1) (side opposite to greater angle is longer)

Angle B and Angle C,

$$AC>AB$$................(2) (side opposite to greater angle is longer)

from equayion 1st and 2nd,

$$AC>BC,AB$$

Hence,hypotenus is longest side.

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Answer 2

The correct statement is,

Prove that in a right-angled triangle the hypotenuse is the greatest side then the other two sides ​

Hence it is proved that, in a right-angled triangle the hypotenuse is the greatest side then the other two sides.

In a right-angled triangle, the angle opposite to the hypotenuse is equal to the 90°, where as, the angles opposite to the sides other than hypotenuse are always less than 90°, i.e., acute angles.

Therefore, in a right-angled triangle, the hypotenuse is the greatest side then the other two sides.