Question

Determine whether a triangle with the following measure theats form a right triangle i) 2cm, 3cm, V3 cm ii) 8 in, loin, 13 in

Answer 1

i) Yes, they do

ii) No, they do not

Here, we want to check if the given triangle lengths form a right triangle

If they form a right triangle, then Pythagoras' theorem will be obeyed

The theorem states that in a right triangle, the square of the hypotenuse (the longest side) equals the sum of the squares of the two other sides

Thus, if we sum the squares of the two lesser number, if they give the square of the larger number, then we have a right triangle

a)

`\begin{gathered} 2^2+3^2\text{ = 4+9 = 13} \\ \text{square root of this is }\sqrt[]{13} \end{gathered}`

These lengths form that of a right triangle

b)

`\begin{gathered} 8^2+10^2\text{ = 64 + 100 = 164} \\ \text{but 13}^2\text{ = 169} \\ So\text{ not equal} \end{gathered}`

We can conclude here that the side lengths do not form that of a right triangle