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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
avatar+24342 
+3

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
 #2
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-3

so what is the answer

 Mar 8, 2020
 #3
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-3

its wrong

 Mar 8, 2020
 #4
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+2

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! smiley

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

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