Question 93267
Starting with the perimeter:
{{{P = 2s+b}}} where s = the length of one of the equal sides and b = the length of the base and P = 29 cm.
But s = 4b-8 s is "8 cm less than 4 times the length of the base"
Substituting 4b-8 for s in the formula for the perimeter:
{{{29 = 2(4b-8)+b}}} Simplify.
{{{29 = 8b-16+b}}}
{{{29 = 9b-16}}} Add 16 to both sides.
{{{45 = 9b}}} Divide both sides by 9.
{{{5 = b}}} This is the length of the base, but you need the length of s, so...
{{{s = 4b-8}}}
{{{s = 4(5)-8}}}
{{{s = 20-8}}}
{{{s = 12}}}cm.

Check:
{{{P = 2(12)+5}}}
{{{P = 24+5}}}
{{{P = 29}}}