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Question

The perimeter of a triangle is 70 cm. The longest side is 6 cm less than the sum of the other two sides. Twice the shortest side is 4 cm less than the longest side. Find the length of each side of the triangle.

Answer 1

x=shortest side

y=middle side

z=longest side

x+y+z=70

z=x+y-6

2x=z-4

in this last equation replace z by x+y-6

2x=x+y-6-4

this becomes...

2x-x-y=-10

x-y=-10

from x+y+z=70, replace z by 2x+4 from equation 2x=z-4 which becomes 2x+4=z

x+y+2x+4=70 and use this with x-y=-10

simplify

3x+y=66

x-y=-10

add the equations

4x=56

x=56/4

x=14 cm

from x-y=-10...

14-y=-10

y=24 cm

14+24+z=70

38+z=70

z=70-38

z=32 cm

14 cm, 24 cm and 32 cm are the sides of the triangle