Question

Please help me with this. (Geometry)

Answer 1

Explanation:

Pythagoras's rule:
`a^2 + b^2 = c^2` becomes
`x^2 + 10^2 = y^2`

If we say b = 10:
`b = 10 = √(c^2 - a^2) = √(y^2 - x^2)`

You only need to look at the left triangle

Which of the options follows Pythagoras's rule?

Let's try the options until we get the right one (in no particular order)

If we try: 3) x = 4 y =
`29√(2)`...

`\sqrt{(29√(2))^2 - 4^4} = 7√(34) \\eq 10`

If we try: 4) x = 16 y = 116...

`√(116^2 - 16^2) = 20√(3) \\eq 10`

If we try: 2) x = 16 y = 29...

`√(29^2 - 16^2) = 3√(65) \\eq 10`

If we try: 1) x = 4 y =
`2√(29)`...

`\sqrt{(2√(29))^2 - 4^2} = 10`