Question

What if one side and hypotenuse of right angled triangle are equal?

Answer 1

Clearly, question asks for the result and effect on the triangle if, one side of a triangle and the hypotenuse of the same triangle are equal to each other.


As we all know, a triangle is a closed figure which has three sides. Sides can be of same length or different length or two sides of same length and one side with different length.

But, in the case of right angled triangles, which have hypotenuse, we generally found that the length of hypotenuse remains greater than the length of other sides.


So,

Now, let a ∆ABC, where AB and BC are the legs( sides which aren't hypotenuse ) and AC is the hypotenuse.


We all are aware of a theorem, known as "Pythagoras Theorem", which states that the length of hypotenuse of a right angled triangle is the square root of the sum of square of other sides.

Mathematically,

Pythagoras theorem says ; hypotenuse = √[ (side${}_1$)^2 + (side${}_2$)^2]


Now coming to our question according to which one side and hypotenuse of a triangle are equal.

From above, sides of the triangle are AB and BC, and hypotenuse is AC.

According to our question, let the side which is equal to the hypotenuse AC be AB.


Therefore, AB = AC

By Pythagoras Theorem :

= > AC^2 = AB^2 + BC^2


Since AC is equal to AB, square of AC is equal to square of AB.

= > AC^2 = AC^2 + BC^2

= > AC^2 - AC^2 = BC^2

= > 0 = BC^2

= > 0 = BC


Since the length of one side is 0.

This is can't be a triangle, as length of one side is 0.

Therefore, this situation can't arise.
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