A triangle has three unequal sides. The
longest side is 3 in. shorter than twice
the length of the shortest side, and the
middle side length is 4.5 in. longer than
half the longest side. If the perimeter of
the triangle is 48 in., what is the
measure of each side?

Step-by-step explanation:

Let's represent the various sides of the triangle as follows;

Longest side is A

Middle side is B

Shortest side is C

From the question,

A = 2C-3

B = (2C-3)/2 + 4.5 = C-1.5+4.5= C+3

Perimeter of a triangle = A+B+C

48In = 2C-3 + C+3 +C

Note that -3+3 =0

48 = 2C+C+C

48= 4C

Divide 48 by the coefficient of C

48/4 = C

C = 12In

Substitute the value of C into the expressions for A and B

A= 2C-3= (2×12)-3= 24-3=21In

B= C+3=12+3=15In

The sides of the triangle are 21in, 15In and 12In respectively