the perimeter of a triangle measures 49 cm. the one side is 7cm longer than the other and 5 cm shorter than the third.find the length of each side.

the perimeter of a triangle measures 49 cm. the one side is 7cm longer than the other and 5 cm shorter than the third.find the length of each side.

Let Side2 be x.
So Side1 will be 7+x
Third side = 49-(x+x+7)= 49-(2x+7)
= 49-2x-7 = 42-2x.
As it is given that Side1 is 5cm shorter than Side3
So Side1= 42-2x-5= 37-2x
So, we can infer that:
37-2x=7+x
37-7=2x+x
30=3x
3x=30
x=30/3
x=10

So, we get to know that:-
Side1=7+x=7+10= 17 cm
Side2=x=10 cm
Side3=42-2x=42-20=22 cm.

And to check, we can add up all the sides and we'll see that they are equal to 49 which is the perimeter.