The perimeter of a rectangle is represented by 8y meters and the area is (6y+3) square meters. a) write two equations in terms of x and y for the perimeter and the area b) determine the perimeter and the area ?

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1 Answer
Apr 6, 2018

Given length of th rectangle l=x+8

width of th rectangle w=x+6

Its perimeter becomes 2(l+w)=8y

2(x+8+x+6)=8y

=>4(x+7)=8y

=>x=2y-7..........[1]

Again area of the rectangle lxxw=6y+3

(x+8)(x+6)=6y+3......[2]

From [1] and [2] we get

(2y-7+8)(2y-7+6)=6y+3

=>(2y+1)(2y-1)=6y+3

=>4y^2-6y-4=0

=>2y^2-3y-2=0

=>2y^2-4y+y-2=0

=>2y(y-2)+1(y-2)=0

=>(2y+1)(y-2)=0

8y being the perimeter y<0 is rejected

So y=2

So perimeter =8y=8xx2=16 m

And area =6y+3=6xx2+3=15m^2