Question

Please help me with 11. I do not know why I got it wrong

Answer 1

In the right triangle, there is a relation between the legs of the right angle and the hypotenuse

$a^2+b^2=c^2$

a and b are the legs of the right angle

c is the hypotenuse

Note that the hypotenuse is the longest side in the right triangle

Since the 3 sides are 6, 12, 13, then

6 and 12 are the legs of the right angle

13 is the hypotenuse

By using the relation above

$\begin{gathered} a=6,b=12 \\ a^2+b^2=(6)^2+(12)^2 \\ a^2+b^2=36+144 \\ a^2+b^2=180 \end{gathered}$$\begin{gathered} c=13 \\ c^2=169 \end{gathered}$

The values of them are not equal as the relation above

$a^2+b^2\ne c^2$

Then 6, 12, 13 can not form sides of a right triangle

We disagree

Because the sum of the squares of the smaller sides is not equal to the square of the longest side.