Question

"the two smaller sides of this right triangle have length 3 and 4, so the hypotenuse must have length 5." this argument is __________.

Answer 1

Since the two smaller sides of the right triangle are 3 and 4, so the hypotenuse must have length 5.

Since in a right triangle, the longer side is hypotenuse and other two sides are base and perpendicular.

Let base = 3, perpendicular = 4 we have to find hypotenuse.

By using Pythagoras theorem, which states

`(Hypotenuse)^(2)=(base)^(2)+(perpendicular)^(2)`

`(Hypotenuse)^(2)=(3)^(2)+(4)^(2)`

`(Hypotenuse)^(2)=9+16`

`(Hypotenuse)^(2)=25`

`Hypotenuse=√(25)`

`Hypotenuse=5`

So, the given argument is correct that the two smaller sides of the right triangle are 3 and 4, so the hypotenuse must have length 5.