Question

do the following which line segments with the given lengths form a right triangle9.40,4111.60,6248.55,73

Answer 1

From the Pythagorean Theorem, if a, b and c are the sides of a right triangle, with c being the longest side, then:

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

Or, equivalently:

$a^2+b^2-c^2=0$

Find the corresponding values of the second expression for each case. If the result is equal to 0, then those are the sides of a right triangle:

9, 40 and 41

$\begin{gathered} 9^2+40^2-41^2=81+1600-1681 \\ =1681-1681 \\ =0 \end{gathered}$

Then, these are the sides of a right triangle.

11, 60 and 62

$\begin{gathered} 11^2+60^2-62^2=121+3600-3844 \\ =3721-3844 \\ =-123 \end{gathered}$

Then, these are not the sides of a right triangle.

48, 55 and 73

$\begin{gathered} 48^2+55^2-73^2=2304+3025-5329 \\ =5329-5329 \\ =0 \end{gathered}$

Then, these are the sides of a right triangle.

Therefore, from the given sets of numbers, the ones that correspond to lengths of sides of a rigtr triangle, are:

$\begin{gathered} 9,40,41 \\ 48,55,73 \end{gathered}$