Question #855d3

Question

2987 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-10T13:04:32

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

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.