Answer:
Possible perimeters:
50 inches, 28 inches, 22 inches, 20 inches.
Step-by-step explanation:
Given that:
Area of triangle = 24 square inches
Side lengths of rectangle are integers.
To find:
Possible perimeter of this rectangle = ?
Solution:
Here, options are missing, so let us calculate all possibilities for the perimeter.
The formula for Area of a rectangle is given as:
[tex]A = Length \times Width[/tex]
Let us make integer factors of 24 first of all.
[tex]24 = 1 \times 24\\24 = 2 \times 12\\24 = 3 \times 8\\24 = 4 \times 6[/tex]
These are the four possibilities of length and breadth.
Let us calculate the possible perimeter for each case using the formula for perimeter:
[tex]Perimeter = 2\times (Length + Width)[/tex]
1st possible option:
[tex]Perimeter = 2\times (1+ 24) = 50\ inches[/tex]
2nd possible option:
[tex]Perimeter = 2\times (2+ 12) = 28\ inches[/tex]
3rd possible option:
[tex]Perimeter = 2\times (3+ 8) = 22\ inches[/tex]
4th possible option:
[tex]Perimeter = 2\times (4+ 6) = 20\ inches[/tex]
