Question

Question #56ff1

Answer 1

With the given measures of 3 and 4 for diagonals and one parallel side 5, parallelogram can not exist.

Explanation:

ABCD is a parallelogram with parallel sides a & b as in the above figure.

Shorter diagonal is d and longer one c

condition 1 : In a triangle, sum of any two sides must be greater than the third side.

Condition 2 : a) In an acute angle triangle, sum of the squares of the two smaller sides will be less than the square of the third side. `c^2 < a^2 + b^2`

b) In a right angle triangle, `c^2 = a^2 + b^2`

c) In an obtuse angle triangle, sum of the squares of the smaller two sides must be less than the square of the third side. `c^2 > a^2 + b^2`

Let's conider triangle ACD with sides a, b, c

It is an obtuse angle triangle as `AhatDC` greater than `90^0`.

`:. c^2 > a^2 + b^2`

But given b = 5, Hence AC = c must be greater than b and hence with diagonal value 3 or 4, the parallelogram can not exist.