Below is a floor plan for a combined living and dining area. The owners of the home have recently adopted a puppy, so the living room needs to be re-carpeted (bad puppy). The total area for both rooms is expressed as LaTeX: 2x^2+x+3 square meters. The tile in the dining room was already replaced, so we know the area of that room is LaTeX: 2x^2-2x square meters. Find an expression for the area that needs to be re-carpeted.

Square metres.

Step-by-step explanation:

The total area of both rooms is given as: Square Metres.

Area of the Dinning Room that was already recarpeted= square meters.

Total Area=Area of Living Room+Area of Dinning Room

=Area of Living Room+

Therefore:

Area of Living Room=

Opening the brackets

=

=

=

Area that needs to be Carpeted= Square metres.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4