The Perimeter Of A Rectangular Backyard Is 6x+6 Yards. If The Width Is X Yards, Find A Binomial That Represents The Length?

The perimeter (p) is given in terms of length (l) and width (w) by
p = 2(l+w)
We are given p and w and want to solve for l
6x+6 = 2(l + x) (substitute known values)
6x + 6 = 2l + 2x (eliminate parentheses using the distributive property)
4x + 6 = 2l (subtract 2x from both sides)
2x + 3 = l (divide both sides by 2)

The length can be represented by 2x+3.

The perimeter of a rectangle has the formula:
Perimeter=2(length + width)
Now lets break the question into parts hence forming equations for both the rectangle's length and its breath as well as its perimeter.
Width=X yards
Length=?
Perimeter=6X+6
Now to find the height of the rectangle lets assume that the alphabet 'L' stands for length and put in the values given in the formula of the perimeter.
Perimeter=2(L+W)
6X+6=2(L+X)
Now we have to make L the subject of the formula. So we would keep it on one side of the equation and shift everything else to the other. Hence,
(6X+6)/2=L+X
L=(6X+6)/2 + X
Hence the binomial that represents the height for the rectangle is (6X+6)/2 + X

(6x + 6)/2 + x = 6x

P = 2 (L+w)
P = 2 (6x + 6)
= 12 x + 6

Half the perimeter of a rectangular garden, whose length is 4meter more than its width,is 36meter. Find the dimensions of the garden.