Question #855d3

1 Answer
Aug 10, 2016

Answer:

#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.