Question

The perimeter of a rectangle is 40 inches. The table shows some of the possible dimensions for the length and area of the rectangle.
Length
(inches)
Area
(square inches)
36
7.5
10
93.75
100
93.75
12.5
18
36

Answer 1

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

$\textrm{Perimeter of Rectangle}=2\times (Length +Width)$

Substituting we get

$40=2(L+W)\\\\L+W=20\\\therefore L=20-W$

We have area of rectangle given as

$\textrm{Area of Rectangle}=Length\times Width)$

Substituting the given values we get

$36=(20-W)\times W\\W^{2}-20W+36=0$

Which is a Quadratic Equation, So by Splitting the middle term we get

$W^{2}-18W-2W+36=0\\W(W-18)-2(W-18)=0\\(W-2)(W-18)=0\\\therefore W=2\ inches\ or\ W =18\ inches$

Therefore the Length will be

$L=20-W=20-2=18\ inches\\OR\\L=20-18=2\ inches$

Therefore the Dimensions are

Length =18 inches and Width = 2 inches

OR

Length =2 inches and Width = 18 inches