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
2007-08-08 06:55:18 · 8 answers · asked by confused 3 in Science & Mathematics ➔ Mathematics
x + x + 2 + x + 4 = 105
3x + 6 = 105
3x = 99
x = 33
The side lengths are 33,35,37
s = (1/2)(33 + 35 + 37) = 52.5
A = sqrt(s(s - a)(s - b)(s - c))
A = sqrt(52.5*(52.5 - 33)*(52.5 - 35)*(52.5 - 37))
A = sqrt(277692.1875) = 526.965
2007-08-08 07:01:18 · answer #1 · answered by pki15 4 · 0⤊ 0⤋
Call the medium side length x.
Then the other sides are length (x-2) AND (x + 2) respectively
(x - 2) + x + (x +2) = 105
3x = 105
x = 35, x- 2 = 33, x + 2 = 37
so the sides are 33, 35, and 37.
Heron's formula states that the area of a triangle is â[s(s-a)(s-b)(s-c)], where s is one half the perimeter and a b and c are the lengths of the sides. the perimeter is 105, so s = 52.5. a = 33, b = 35, c = 37
Entering sqrt(52.5*(52.5-33)*(52.5-35)*(52.5-37)) in google calculator gives a result of 526.965072
2007-08-08 14:07:04 · answer #2 · answered by Edgar Greenberg 5 · 0⤊ 0⤋
well lets put this into street term for better understanding for the common folk out there well if bubba had a perimeter of 105 inches in length. it would form a triangle behind him of ladies waiting in line. although some might be a odd interger. using herons hernia formula the area for buba's pad is a direct reflection of the length and the perimeter. therefor 105 inches is equal to area of a 12 x 12 room which bubba could fir up to 50 fine looking ones. at a rate of 20 per the awnser is 12.3756 another problem solved by luigi the diver
2007-08-08 14:04:16 · answer #3 · answered by Anonymous · 0⤊ 0⤋
x + (x+2) + (x+4) = 105 because x is the 1st odd integer and consecutive odd integers are two apart
so 3x + 6 = 105
and 3x = 99
so x = 33 and your 3 consecutive odd intergers are:
33, 35, 37
These are the lengths of the 3 sides of the triangle, use thes with Heron's Formula
2007-08-08 14:01:19 · answer #4 · answered by Steve P 5 · 0⤊ 0⤋
not sure on the heron's formula, but the sides are 33, 35, 37
2007-08-08 13:59:48 · answer #5 · answered by csmithballsout 4 · 0⤊ 0⤋
the sides are 33, 35, and 37 inches, but I don't know what Heron's formula is..
2007-08-08 13:58:20 · answer #6 · answered by smartee 4 · 0⤊ 0⤋
7
2007-08-08 13:57:28 · answer #7 · answered by Anonymous · 0⤊ 1⤋
33, 35, 37
I assume you mean Hero's Formula which would be
Area^2=S(S-A)(S-B)(S-C) where A,B,and C are the three sides and S=(1/2)(A+B+C)
2007-08-08 14:00:00 · answer #8 · answered by Anonymous · 0⤊ 0⤋