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# DUDE HELP ME OUT

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In a certain isosceles triangle, the base is $1\frac 12$ times as long as each leg and the perimeter is $63.$ How long is the base?

Mar 8, 2020

#1
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isosceles triangle   means two legs are the same length     and base is 1/12 as long as leg

x = leg length

x + x  + x/12  =63     solve fo 'x' the leg length    then base = x/12

Mar 8, 2020
edited by ElectricPavlov  Mar 8, 2020
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Mar 8, 2020
#3
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its wrong

Mar 8, 2020
#4
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Let's try setting x equal to the length of each leg. Then, we have two sides of length x and one of length $$\dfrac 32\cdot x,$$ so the perimeter is $$x+x+\dfrac 32\cdot x,$$which is  $$\dfrac 72\cdot x.$$We also know the perimeter is  63 so we set our two expressions for the perimeter equal to each other: $$\frac 72\cdot x = 63.$$
Multiplying both sides by $$\frac{2}{7}$$ gives  The base is $$1\frac 12\cdot 18 = \boxed{27}$$

Hope it helps!

Mar 10, 2020
edited by TechnoWizard  Mar 10, 2020
edited by TechnoWizard  Mar 17, 2020