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?
+36915 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
+4 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! 
