Respuesta :
Answer:
Therefore the Dimensions are
Length =18 inches and Width = 2 inches
OR
Length =2 inches and Width = 18 inches
Step-by-step explanation:
Let the Width of rectangle be 'W' inches.
The length of a rectangle be 'L' inches.
Area of rectangle given is 36 square inches.
Perimeter of Rectangle is 40 inches.
To Find:
Length = L = ?
Width = W = ?
Solution:
Perimeter of Rectangle is given as
[tex]\textrm{Perimeter of Rectangle}=2\times (Length +Width)[/tex]
Substituting we get
[tex]40=2(L+W)\\\\L+W=20\\\therefore L=20-W[/tex]
We have area of rectangle given as
[tex]\textrm{Area of Rectangle}=Length\times Width)[/tex]
Substituting the given values we get
[tex]36=(20-W)\times W\\W^{2}-20W+36=0[/tex]
Which is a Quadratic Equation, So by Splitting the middle term we get
[tex]W^{2}-18W-2W+36=0\\W(W-18)-2(W-18)=0\\(W-2)(W-18)=0\\\therefore W=2\ inches\ or\ W =18\ inches[/tex]
Therefore the Length will be
[tex]L=20-W=20-2=18\ inches\\OR\\L=20-18=2\ inches[/tex]
Therefore the Dimensions are
Length =18 inches and Width = 2 inches
OR
Length =2 inches and Width = 18 inches
