A triangle has a perimeter of 105 inches. The lengths of the sides of the triangle are consecutive odd integer

Question

A triangle has a perimeter of 105 inches. The lengths of the sides of the triangle are consecutive odd integers. Find the length of the sides and then use Heron’s Formula to find the area of a triangle. Show all work to receive credit.

Answer 1

First, divide the perimeter by 3
This means the average length of an edge is 35
Therefore the consecutive odd integers are 33, 35 and 37

Using Herons Formula, the area is

A= Squroot[(105/2) * (105/2-35) * (105/2-33) * (105/2-37)]

Note: I corrected this. Despite too many years of education, I could not divide 105 by 3 :-)

Answer 2

let the sides be a, b and c defined as:
a=(2n+1), b=(2n+3) and c=(2n+5)
perimeter = 2n+1+2n+3+2n+5 = 6n+9
6n+9 =105 ~~~> n = 16

a=2n+1 =33
b =35
c=37
let s = (a+b+c)/2= 52.5


Heron's formula Heron's formula for the area of a triangle with sides of length a, b, c is

A = sqrt{s(s-a)(s-b)(s-c)}
A = sqrt{52.5(19.5)(17.5)(15.5)} = sqrt(277692.1875)= 526.965 inch^2