The equation that the scarecrow uttered can be expressed
mathematically as:
sqrt (C) = sqrt (A) + sqrt (B)
where A, B, and C are the sides of the triangle
Since the triangle is an isosceles, therefore A = B and
sqrt (C) = 2 sqrt (A)
given that the measure of the leg is 3, A = 3, C is:
sqrt C = 2 sqrt (3)
sqrt C = 3.464
C = 12
In a any triangle, the sum of two sides must be greater
than the third side, since in this case C > A + B therefore the Scarecrow is
not correct because the correct relationship should be A + B > C.
To find the correct hypotenuse, we start with the
Pythagorean equation:
C^2 = A^2 + B^2
So what the scarecrow mistakenly did was to ignore the “+”
symbol during the square root. Taking the square root on both sides, the
correct equation is:
C = sqrt (A^2 + B^2)
Calculate for C, since A = B = 3:
C = sqrt (3^2 + 3^2)
C = 4.24
So now A + B > C and this is now correct.
