Answer:
[tex]a=180\\b=60\\c=130[/tex]
Step-by-step explanation:
First side = a
Second side = b
Third side = c
a is three times as long as the b (a=3b). C is 50 cm shorter than a (c=50-a)
The perimeter is 370cm (a+b+c=370)
[tex]a=3b\\c=a-50\\a+b+c=370[/tex]
Take [tex]a=3b[/tex] and solve for b;
[tex]b=\frac{a}{3}[/tex]
Now b is in terms of a, and c is in terms of a, therefore if we replace in the last equation all these values, we can find a.
[tex]a+b+c=370\\a+\frac{a}{3}+a-50 =370\\2a+\frac{a}{3}-50=370[/tex]
[tex]\frac{(2a)(3)+a}{3} =\frac{7}{3}a-50=370[/tex]
Add 50 on both sides.
[tex]50+\frac{7}{3}a-50=370+50[/tex]
[tex]\frac{7}{3}a=420[/tex]
Multiply by the reciprocal of [tex]\frac{7}{3}[/tex]. The reciprocal of a fraction is the inverted fraction. Therefore it is: [tex]\frac{3}{7}[/tex]
[tex]\frac{3}{7}*\frac{7}{3}a=420*\frac{3}{7}[/tex]
[tex]a=180[/tex]
Now replace a in the equation [tex]b=\frac{a}{3}[/tex] to find b.
[tex]b=\frac{a}{3}[/tex]
[tex]b=\frac{180}{3} \\b=60[/tex]
Finally, replace a in the equation [tex]c=a-50[/tex] to find c
[tex]c=a-50\\c=180-50\\c=130[/tex]
