Respuesta :
The area of a rectangle can be determined by the following equation:
[tex]\text{Area = Lenght }\times\text{ Width}[/tex]First statement: The rectangle can have a length of 10 inches and a width of 3 inches (True!).
[tex]\text{Area = 10}\times3\text{ = 30 square inches}[/tex]Second statement: The rectangle can have a length of 7 inches (False!). If the Area must be 30 square inches and the length and width of each rectangle are whole numbers of inches:
[tex]30\text{ = 7}\times\text{Width}[/tex][tex]\text{Width = 4.28}[/tex]Width is not a whole number.
Thrid statement: The rectangle can have a width of 2 inches (True!)
[tex]30\text{ = 2}\times\text{Length}[/tex][tex]\text{Length = 15}[/tex]Fourth statement: The rectangle can have a length of 12 inches, a width of 3 inches, and a perimeter equal to its area (False!)
[tex]\text{Area = 12}\times3\text{ = 36 }\ne30[/tex]Fifth statement: The rectangle can have a width of 5 inches and a perimeter that is less than 30 inches (True!). Suppose that the length is 6 inches. The perimeter would be 5+5+6+6 = 22 inches and the area:
[tex]\text{Area = 5}\times6\text{ = 30 square inches}[/tex]Therefore, the answers will be True-False-True-False-True.
