1. An open box is to be made from a sheet of card 40cm by 30cm. A square of side x cm is to be cut from each corner, as shown in the diagram, and then the sides will be folded up so that the
depth of the box will be x cm.

(a) Find in terms of x the length and width of the base of the box (ie AB and AD).
(b) The volume of the box is y. Write down an equation expressing y in terms of x.​

Step-by-step explanation:

AB = DC = 40 - 2x

AD = BC = 30 - 2x

there is not more explanation possible, I think.

we cut off from each side 2 pieces of x cm. so, AB, DC, AD, BC are the the remaining lengths.

the volume of the box is ground area times height (x is the length of the remaining flaps after the cut, so, when folding up these flaps/sides, they will be x cm high).

Volume = y = AB×AD×x

=> y = (40-2x)×(30-2x)×x = (1200 - 60x - 80x + 4x²)×x =

= (1200 - 140x + 4x²)×x = 4x³ - 140x² + 1200x

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!