Answer:
The shorter side is 5 inches and the longer side is 8 inches.
Step-by-step explanation:
We start by listing formulas for solving for the area and perimeter of a rectangle, which will then determine how we find the dimensions we are looking for.
The area of a rectangle is length (l) times width (w), often represented as:
A = l(w), or A = lw
The perimeter of a rectangle is the sum of twice the length and twice the width, often represented as:
P = 2l + 2w
If product of length and width is 40 inches per the rectangle's given area, then a factor pair of 40 must be the dimensions of the rectangle. These values can then be checked to see if they also satisfy the perimeter of the rectangle.
So first, list factors of 40:
1, 40; 2, 20; 4, 10; 5, 8
Now, we plug these pairs into the perimeter equation.
2(1) + 2(40) = 2 + 80 = 82
82 > 26
2(2) + 2(20) = 4 + 40 = 44
44 > 26
2(4) + 2(10) = 8 + 20 = 28
28 > 26
2(5) + 2(8) = 10 + 16 = 26
26 = 26
Therefore, the factors 5 and 8 are what we use. 5 inches by 8 inches are the dimensions.