Question

The first side of a triangle is three times as long as the second side, and the third side is 50 cm shorter than the first side. Find all sides of triangle if its perimeter is 370 cm.

Answer 1

`a=180\\b=60\\c=130`

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)

`a=3b\\c=a-50\\a+b+c=370`

Take
`a=3b` and solve for b;

`b=(a)/(3)`

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.

`a+b+c=370\\a+(a)/(3)+a-50 =370\\2a+(a)/(3)-50=370`

`((2a)(3)+a)/(3) =(7)/(3)a-50=370`

Add 50 on both sides.

`50+(7)/(3)a-50=370+50`

`(7)/(3)a=420`

Multiply by the reciprocal of
`(7)/(3)`. The reciprocal of a fraction is the inverted fraction. Therefore it is:
`(3)/(7)`

`(3)/(7)*(7)/(3)a=420*(3)/(7)`

`a=180`

Now replace a in the equation
`b=(a)/(3)` to find b.

`b=(a)/(3)`

`b=(180)/(3) \\b=60`

Finally, replace a in the equation
`c=a-50` to find c

`c=a-50\\c=180-50\\c=130`