Question

A rectangular packet of drink has a width that is 2 cm less than its length.

Its height is 4 cm more than its length.
(a) It is given that the length of the packet is m cm. Write down an expression,
in terins of m, for the total surface area of the packet.
[2]​

Answer 1

`6m^2+8m-16`

Explanation:

Given that the length of the packet is
`l=m` cm.

Then the width being 2cm less than the length becomes
`w=m-2` and the height being 4 cm more than its length becomes
`h=m+4`

The total surface area of the rectangular packet is given by:

`T.S.A=2(lw+lh+wh)`

`\implies T.S.A=2[m(m-2)+m(m+4)+(m-2)(m+4)]`

We expand to get:

`\implies T.S.A=2(m^2-2m+m^2+4m+m^2+4m-2m-8))`

`\implies T.S.A=2(3m^2+4m-8)=6m^2+8m-16`