Can the sides 30, 40, 50 be a right triangle?

Jun 10, 2015

If a right angled triangle has legs of length $30$ and $40$ then its hypotenuse will be of length $\sqrt{{30}^{2} + {40}^{2}} = 50$.

Explanation:

Pythagoras's Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.

${30}^{2} + {40}^{2} = 900 + 1600 = 2500 = {50}^{2}$

Actually a $30$, $40$, $50$ triangle is just a scaled up $3$, $4$, $5$ triangle, which is a well known right angled triangle.

Jun 10, 2015

Yes it can.

Explanation:

To find out whether the triangle with sides 30, 40, 50, you would need to use the Pythagoras theorem ${a}^{2} + {b}^{2} = {c}^{2}$ (equation for calculating unknown side of a triangle).
Substituting the variables we get the equation ${30}^{2} + {40}^{2} = {c}^{2}$ we won't substitute 50. because we are trying to find whether this equals 50
${30}^{2} + {40}^{2} = {c}^{2}$
$2500 = {c}^{2}$
$\sqrt{2500} = c$
$50 = c$
Therefore because 'c' equals 50 we know that this triangle is a right triangle.