Answer:
Step-by-step explanation:
w and d are the width and diagonal, respectively.
w = d/2 + 1 = (d+2)/2
Pythagorean theorem
w^2 + 8^2 = d^2
substitution
(d+2)^2/4 +64 = d^2
(d+2)^2 + 256 = 4d^2
d^2+4d+4 + 256 = 4d^2
3d^2-4d-260 = 0
Quadratic formula
d = [4±√( 4²-4(3)(-260))]/[2⋅3] = 10, -26/3
-26/3 is an extraneous solution, so d = 10 inches
w=d/2 +1 =6 inches
Ant‘s path = 8+6 = 14 inches
Beetle’s path = 10 inches
14 < 1.5(10)
Ant reaches food first.
