Question

A 30-inch segment is cut into two parts whose lengths have the ratio 3 to 5. find the length of the shortest part?

Answer 1

The length of the shortest part is;
$\frac{3}{8} *30= 11.25 inches$

Answer 2

Let x be the common factor between the two lengths. The length of the shorter part is 3x and that of the remaining side is 5x. The lengths of these two parts should sum up to 30 in. The equation relating them is,

                                   3x + 5x = 30

The value of x is 3.75. The shorter side is 3x or (3)(3.75) in. Thus, the shorter side is 11.25 inches.