Answer: The perimeter is 30ft.
Step-by-step explanation:
Let's define:
L = length of the longer side.
S = length of the shorter side.
P = perimeter
we know that for a common rectangle:
P = 2*S + 2*L
We aso know that:
L = 2ft + (1/3)*P
S = (1/10)*P
L = S + 9ft.
So we have a system, let's find the perimeter only using this system (So i will ignore the equation for the perimeter of a rectangle)
First, we can replace the third equation in the first equation, now we have a system with only two equations:
S + 9ft = 2ft + (1/3)*P
S = P/10
Now we can replace the second equation in the first equation, and get:
P/10 + 9ft = 2ft + P/3
Now let's solve this for P.
9ft - 2 ft = P/3 - P/10
7ft = P( 1/3 - 1/10) = P*( 10/30 - 3/30) = P*(7/30)
(30/7)*7ft = P = 30ft.
The perimeter is 30ft.
