Question:
The first side of a triangle is four inches longer than twice the
second side. The third side of the triangle is 5 inches shorter than
the sum of the other two sides. The perimeter is 72 inches. Find
the lengths of the three sides.
Answer:
The sides of the triangle are: 11.5, 27 and 33.5
Step-by-step explanation:
Let the first side be f, the second be s and the third be t.
So, we have:
[tex]f =4 + 2s[/tex]
[tex]t = f + s - 5[/tex]
[tex]Perimeter = 72[/tex]
Required
Determine the length of the three sides
Perimeter is calculated as:
[tex]Perimeter = f + t + s[/tex]
Substitute values for f and t
[tex]Perimeter = 4+2s + f+s-5 + s[/tex]
[tex]Perimeter = f+2s +s+s-5+4[/tex]
[tex]Perimeter = f+4s-1[/tex]
Substitute values for f and Perimeter
[tex]72 = 4+2s+4s-1[/tex]
[tex]72 = 2s+4s-1+4[/tex]
[tex]72 = 6s+3[/tex]
Collect Like Terms
[tex]6s = 72 -3[/tex]
[tex]6s = 69[/tex]
[tex]s= 11.5[/tex]
[tex]f =4 + 2s[/tex]
[tex]f = 4 + 2 *11.5[/tex]
[tex]f = 27[/tex]
[tex]t = f + s - 5[/tex]
[tex]t=27+11.5 - 5[/tex]
[tex]t=33.5[/tex]
The sides of the triangle are: 11.5, 27 and 33.5
