Question

This is due tomorrow! Can someone help?

Answer 1

`(6x - 4)` units

Explanation:

A = Area of rectangle

=
`(2x^(2) -11x - 63)` square units

L = Length of rectangle

=
`(2x + 7)` units

B = Breadth of rectangle

= Unknown

P = Perimeter of rectangle

= Unknown

Area of a rectangle = Length × Breadth

A = L × B

Which means:

B =
`(A)/(L)`

=
`(2x^(2) -11x - 63)/(2x + 7)`

`(2x^(2) - 11x - 63)` is a quadratic expression which can be factorised using the Double Bubble method and one of the two factors is the expression
`(2x + 7)`

Double Bubble Method:

Multiple 2 and 63 to give 126. Write down a complete list of pairs of factors of 126 and choose the most suitable and appropriate pair of factors that would add or subtract to give 11. The selected pair of factors are 18 and 7. These two will be used to rewrite
`-11x`:

`2x^(2) - 11x - 63`

`2x^(2) - 18x + 7x - 63`

Apply factorization by grouping:

`2x(x - 9) + 7(x - 9)`

Extract the common factor expression
`(x -9)`:

=
`(x - 9)(2x + 7)`

This means:

L = Length of rectangle =
`2x + 7`

B = Breadth of rectangle =
`x - 9`

∴P = 2 × (L + B)

=
`2[(2x + 7) + (x - 9)]`

Expand the parenthesis by using the Distributive Law and bring like terms together and simplify them in their lowest forms:

`= 2[2x + 7 + x - 9]`

`= 4x + 14 + 2x - 18`

`= 4x + 2x + 14 - 18`

∴P = Perimeter of rectangle
`= (6x - 4)` units