Question 113273
Let x=length of base, y=length of equal legs


Since one of the equal legs is 8 cm less than four times the base the base, we get


Equal Leg: {{{y=4x-8}}}



Now simply add the base to two equal legs like this:


{{{x+y+y=29}}}


{{{x+2y=29}}} Combine like terms



{{{x+2(4x-8)=29}}} Plug in {{{y=x-8}}}





{{{x+8x-16=29}}} Distribute



{{{9x-16=29}}} Combine like terms on the left side



{{{9x=29+16}}}Add 16 to both sides



{{{9x=45}}} Combine like terms on the right side



{{{x=(45)/(9)}}} Divide both sides by 9 to isolate x




{{{x=5}}} Divide


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Answer:

So our answer is {{{x=5}}} 



So this means the base is 5 cm


{{{4*5-8=20-8=12}}} Now plug in {{{x=5}}} into {{{y=4x-8}}} to find the equal leg's length.



So the equal legs are 12 cm each



Check:


The sum of the sides should be 29, so let's verify:


{{{5+12+12=29}}} Plug in the solved values into the perimeter formula



{{{29=29}}} Add. Since both sides are equal, our answer is verified.