Question

Question #855d3

Answer 1

`x = (54 -sqrt(2196))/8`

Explanation:

We need to choose and define a variable.

Let the width of the border be `x` metres.

Now we can define the length and width of the mural, remembering that the border is on both sides.

Length of mural = `(15-2x)` metres
width of mural = `(12-2x)` metres

The area of the wall is `15xx12 = 180m^2`

The area of the mural is 75% of this: `0.75 xx180 = 135m^2`

Now we have enough information to write an equation and solve it.

`Area = l xx b =135`

`(15-2x)(12-2x) = 135`

`180-30x-24x +4x^2 -135=0`

`4x^2 -54x +45 = 0`

Using the formula:

`x = (-b+-sqrt(b^2-4ac))/(2a)`

`x = (-(-54) +-sqrt((-54)^2 -4(4)(45)))/(2xx4)`

`x = (54 +-sqrt((-54)^2 -720))/8`

`x = (54 +-sqrt(2196))/8`
Estimating which value we should use gives the following:

`x~~ (54+50)/8 = ~~13`

`x~~ (54-50)/8 ~~ 0.5`

Obviously we cannot subtract 13 twice from either the length or the width, so the second answer is the one we need.