SOLUTION: the perimeter of a triangle is 90 cm. The measure of the longest side is 6 less than the sum of the measures of the other two sides. Four times the measure of the shortest side equ

Algebra ->  Triangles -> SOLUTION: the perimeter of a triangle is 90 cm. The measure of the longest side is 6 less than the sum of the measures of the other two sides. Four times the measure of the shortest side equ      Log On


   

Question 302592: the perimeter of a triangle is 90 cm. The measure of the longest side is 6 less than the sum of the measures of the other two sides. Four times the measure of the shortest side equals the sum of the other two sides. what is the length in cm of the shortest side of the triangle?
Answer by london maths tutor(243) About Me  (Show Source):
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Let's the longest length be "a", the shortest be "c" and the other length be "b"
the perimeter of a triangle is 90 cm
a + b + c = 90 ... equation 1
Longest side is 6 less than the sum of the measures of the other two sides:
(b + c)-6 = a ... equation 2
Four times the measure of the shortest side equals the sum of the other two sides:
4c = a + b ... equation 3
Put equation 3 into equation 1:
4c + c = 90
5c = 90
c = 18 cm
The shortest length is 18cm.