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

$(Hypotenuse)^{2}=(base)^{2}+(perpendicular)^{2}$

$(Hypotenuse)^{2}=(3)^{2}+(4)^{2}$

$(Hypotenuse)^{2}=9+16$

$(Hypotenuse)^{2}=25$

$Hypotenuse=\sqrt{25}$

$Hypotenuse=5$

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.