Question

One of the sides of a parallelogram has the length of 5 in. Can the lengths of the diagonals be: 4 in and 3 in?

Answer 1

No, the lengths of the diagonals cannot be 4 in and 3 in.

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

`2AB^2 +2BC^2 = AC^2 +BD^2` ----------------------(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)

`2(5)^2 +2BC^2 = 4^2+3^2`

`2(25)+2BC^2 = 16+5`

`50 + 2BC^2 = 16+5`

`50 + 2BC^2 =25`

Now this is not possible and does not satisfy the parallelogram ,Thus the diagonals cannot be 3 inches and 4 inches