Find the value of p and of q, such that q > p in the following case:
An open rectangle tank that measures p*p*q m^3 is made of metal sheets. It is given that the area of the metal sheets needed to construct the tank is 7m^2 and the total length of all the sides of the tank is 14m.
The open rectangular tank has sides measuring (in m) p, q and p where p and q are the sides of the base and p is the height.
It is given that the length of all the sides is 14 m,
=> 2p + q = 14
Also, the area of the metal sheets required is 7 m^2.
=> p*q + 2*p*p + 2*p*q = 7
=> 3pq + 2p^2 = 7
Substitute q = 14 - 2p
=> 3p*(14 - 2p) + 2p^2 = 7
=> 42p - 6p^2 + 2p^2 = 7
=> 42p - 4p^2 = 7
=> 4p^2 - 42p + 7 = 0
Solving the equation gives p = `(21 - sqrt 413)/4` and p = `(21 + sqrt 413)/4`
As q > p, take p = `(21 - sqrt 413)/4` . As q = 14 - 2p, q = `14 - (21 - sqrt 413)/2 = (7 + sqrt 413)/2`
The value of p = `(21 - sqrt 413)/4 ` and q = `(7+sqrt 413)/2`