Answer:
No, the lengths of the diagonals cannot be 4 in and 3 in.
Step-by-step explanation:
The parallelogram law which is also known as parallelogram identity states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals.
According to the law,In the following figure
[tex]2AB^2 +2BC^2 = AC^2 +BD^2[/tex] ----------------------(1)
In the question it is stated that,
one side is 5 inches. So lets assume AB = 5
The Diagonals are 4 and 3 inches
Let AC be 4 inches and BD be 3 inches
Substituting the given values in (1)
[tex]2(5)^2 +2BC^2 = 4^2+3^2[/tex]
[tex]2(25)+2BC^2 = 16+5[/tex]
[tex] 50 + 2BC^2 = 16+5[/tex]
[tex] 50 + 2BC^2 =25 [/tex]
Now this is not possible and does not satisfy the parallelogram ,Thus the diagonals cannot be 3 inches and 4 inches
