Question

The tip of a toy arrowhead shaped as an isosceles right triangle is sketched on a graph. The endpoints of one leg are (0,0) & (0,8). What is the length of the longest side of the tip?

Answer 1

The two points mentioned in the problem are represented in the following image:

We are told that the triangle must be an isosceles right triangle, this means that:

to be an isosceles it must have 2 equal legs

to be a right triangle it must have a 90° angle.

In the previous image we can see that the vertical leg has a length of 8.

So the other leg must also have a length of 8:

As we can see we have the two things: two equal sides (isosceles ) and a 90° angle ( right triangle).

Thus, the longest side must be the hypotenuse of the triangle, which we find using the Pythagora's theorem:

To find the hypotenuse with Pythagora's theorem we take the square root of the legs squared as we see in the previous image.

Now we solve that to find the length:

`\begin{gathered} =\sqrt[]{8^2+8^2} \\ =\sqrt[]{2(8^2)} \\ =\sqrt[]{2}\sqrt[]{8^2} \\ =8\sqrt[]{2} \end{gathered}`

Answer: the length of the longest side of the tip is

`8\sqrt[]{2}`