Question

Complete the work to find the dimensions of the rectangle. x(x – 3) = 10 x2 – 3x = 10 x2 – 3x – 10 = 10 – 10 (x + 2)(x – 5) = 0 What are the width and length of the rectangle?

Answer 1

`Length =5`

`Width = 2`

Explanation:

Given

`Length =x`

`Width = x -3`

`Area = 10`

`x(x-3) =10`

See comment for missing part of the question

Required

Complete the expression to determine the dimension of a rectangle

We have:

`x(x-3) =10`

Open bracket

`x^2 -3x = 10`

Equate to 0

`x^2 -3x - 10 =0`

Expand

`x^2 + 2x - 5x - 10 = 0`

Factorize

`x(x + 2) - 5(x + 2) = 0`

Factor out x + 2

`(x - 5)(x + 2) = 0`

Solve for x

`x - 5 = 0` or
`x + 2 = 0`

`x = 5` or
`x = -2`

The value of x cannot be negative

So:

`x = 5`

Recall that:

`Length = x`

`Width = x - 3`

So:

`Length =5`

`Width = 2` ---- i.e. 5 - 3