The ratio of the measures of three sides of a triangle is 1/4: 1/3: 1/6. its perimeter is 31.5 inches.

The correct question is
The ratio of the measures of three sides of a triangle is 1/4:1/3:1/6. its perimeter is 31.5 inches. Find the measure of each side of the triangle

we know that

Just as the ratio 1/4:1/3:1/6 is equivalent to (1/4)x:(1/3)x:(1/6)x
so
31.5= (1/4)x+(1/3)x+(1/6)x> 31.5=x*(6+8+4)/24> 31.5=18x/24
x=24*31.5//18> x=42 in

the answer is
the measure of each side is
(1/4)x (1/4)*42> 10.5 in
(1/3)x (1/3)*42> 14 in
(1/6)x (1/6)*42> 7 in

Hope i can you!

The first option would be correct if it were one half and not one