Geometry Help please

Question

The perimeter of a triangle is 45 feet. The ratio of the width to the length is 2:3:4. Find the measure of each side.

 

x=      a=       b=      c=

 

i have to show work 

Answer 1

Let a, b, and c be the sides of the triangle from smallest (a) to largest (c).

 

The ratio of side b to a is:

 

      b       3

     --- = ---

      a       2

 

     So b = (3/2)a = (1.5)a

 

The ratio of side c to a is:

 

      c      4

     --- = ---

      a      2

 

     So c = (4/2)a = 2a

 

The perimeter is 45 feet:

 

     a + b + c = 45

 

Substitute 1.5a for b and 2a for c:

 

     a + (1.5)a + 2a = 45

     4.5a = 45

 

     a = 10 ft

     b = (1.5)a = (1.5)(10) = 15 ft

     c = 2a = 2*10 = 20 ft

 

Check:

 

     10 + 15 + 20 = 45

     45 = 45