Full answer to: The two shorter sides of a right triangle are (2+√2)cm and (2+√2)cm. Determine the length of the longest side, written as a simplified surd.

Answer 1

hypotenuse squared = sum of squares of the other two sides

c^2 = a^2 + b^2

c = sqr(a^2 +b^2) if a=b = 2+sqr2 then

c = sqr((2+sqr2)^2 + (2+sqr2)^2) = sqr(4 +4sqr2 +2 + 4+4sqr2 + 2) = sqr(12 +8sqr2)

longest side = square root of (12+8sqr2) = about 4.828 cm

the shorter sides = 2+sqr2 = about 3.1414

(3.414)^2 + (3.414)^2 = 23.312

longest side = sqr23.312 = about 4.828 cm

exact answer is 12+8sqr2 cm