Question

What is the width of the rectangle?

The area of a rectangle is 72 cm². The length of the rectangle is 6 cm longer than the width.

What is the width of the rectangle?

A. 2 cm

B. 6 cm

C. 8 cm

D. 10 cm

Answer 1

`"C."` `6` `"cm"`

Explanation:

Let the width of the rectangle be `x`.

The length of the rectangle is `6` `"cm"` longer than the width:

`Rightarrow "Length" = x + 6` `"cm"`

Also, the area of the rectangle is `72` `"cm"^(2)`:

`Rightarrow "Area" =` `"length"` `times` `"width"`

`Rightarrow 72 = (x + 6) times x`

`Rightarrow 72 = x^(2) + 6 x`

`Rightarrow x^(2) + 6 x - 72 = 0`

Using the quadratic formula:

`Rightarrow x = frac(- 6 pm sqrt(6^(2) - 4(1)(- 72)))(2(1))`

`Rightarrow x = frac(- 6 pm sqrt(36 + 288))(2)`

`Rightarrow x = frac(- 6 pm sqrt(324))(2)`

`Rightarrow x = frac(- 6 pm 18)(2)`

`Rightarrow x = - 12, 6`

However, the width of the rectangle cannot be a negative number, i.e. `x ne - 12`.

So `x = 6` is the solution to the equation.

Therefore, the width of the rectangle is `6` `"cm"`.

Answer 2

Width = `6cm` which is B

Explanation:

Let the width be `x`, because we know the length is `6cm` longer.

Width = `x` and length =`x+6`

Area = length x width, and we know it is `72cm^2`

`x xx(x+6)=72`

`x^2 +6x -72 =0" "larr` make a quadratic equal to `0`

To solve the quadratic equation, try to factorise first.

To factorise, find factors of `72` which differ by `6`

`12xx6 = 72 and 12-6 =6`

`(x+12)(x-6)=0`

Set each factor equal to `0`

`x+12 =0`

`rarr x = -12" "larr` reject as width cannot be negative

`x-6=0`

`rarr x =6cm" larr` this is the width.

The correct option is `B`

Check: width = `6cm and` length `=6+6=12cm`

Area = `12cmxx 6cm=72cm^2`