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What is the length of the shortest side of Δabc whose perimeter is 64 units if the ratio ab to bc is 4to3 and ac is 20 less than the sum of the lengths of sides ab and bc?
Wiki User
∙ 11y ago
It is customer to use capital letters for the vertices of a triangle, and lower case letters for the sides, with a being opposite A etc. So AB is c and so on. Converting the letters in the problem to capitals, and using a for BC and so on, we have 3 linear equations in a, b, and c, namely
a + b + c = 64
c = (4/3)a
b = a + c - 20
Substituting the second equation into the third gives
b = (7/3)a - 20
Substituting this and the second equation into the first gives
a + (7/3)a - 20 + (4/3)a = 64
Simplifying,
(14/3)a - 20 = 64
(14/3)a = 84
a = 18
b = 22
c = 24
The answer is 18
Wiki User
∙ 11y ago
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