Question

Tell whether the triangle with the given sides lengths is a right triangle

Answer 1

If this is a right triangle, then $a^{2}+ b^{2}= c^{2}$ where c is the hypotenuse which is ALWAYS THE LONGEST SIDE.  Our longest side is 5, so we will set up Pythagorean's Theorem to see if the addition of the squares of a and b = the square of c: $(1.4)^{2} +(4.8) ^{2} =(5)^{2}$.  Squaring all of that and adding on the left gives us 25=25.  Because this is true, we have proven the converse of the Pythagorean Theorem here and this is a right triangle.