I need help with this question

Question

The longest side of a triangle is 8ft longer than three times the length of the shortest side. The other side of the triangle is 8ft shorter than three times the length of the shortest side. Find the lengths of the sides of the triangle.

Answer 1

L = 3s = Longest side of a triangle

m = 3s-8 = middle sized side of the same triangle

s = shortest side of the triangle

what are the 3 side lengths??

3 sides in terms of s are

3s, 3s-8 and s

use law of cosines and/or sines

(3s)^2 = (3s-8)^2 + s^2 - 2(3s-8)(s)CosL

9s^2 = 9s^2 -48s +64 +s^2 -(6s-16)sCosL

s^2 -6s^2CosL +16sCosL + 64= 0

s =-16CosL/(2-12CosL) +/-(1/(2-12CosL)sqr(16^2Cos^2L -4(64)(1-6CosL))

= shortest side

if it's a right triangle then

about 141 -133 -47

or 138 - 1380 -46

or somewhere in between

maybe about 140 - 132 - 46.6