Question

The area of a rectangle is represented by (x^2-14x-32) square units . If the width of the rectangle is represented by (x+2) units , which expression represents the length of the rectangle

Answer 1

The expression for length of rectangle is (x - 16) units

Solution:

Given that area of a rectangle is represented by
`x^2-14x-32` square units

width of the rectangle is represented by (x+2) units

To find: length of the rectangle

The area of rectangle is given as:

`\text { area of rectangle }=\text { length } * \text { width }`

Substituting the values in formula, we get

`x^(2)-14x-32=\text{length} *(x+2)` ---- eqn 1

Let us first factorise the L.H.S of eqn 1

`x^(2)-14x-32`

Break the expression into groups

`=\left(x^2+2x\right)+\left(-16x-32\right)`

`\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+2x\mathrm{:\quad }x\left(x+2\right)`

`\mathrm{Factor\:out\:}-16\mathrm{\:from\:}-16x-32\mathrm{:\quad }-16\left(x+2\right)`

`=x\left(x+2\right)-16\left(x+2\right)`

`\mathrm{Factor\:out\:common\:term\:}x+2`

`=\left(x+2\right)\left(x-16\right)`

Now substitute the above value in eqn 1

`(x + 2)(x - 16) = length * (x + 2)`

`length = ((x + 2)(x - 16))/(x + 2)`

Length = x - 16

Thus the expression for length of rectangle is (x - 16) units