Question

A parallelogram ABCD has the area of 40 cm2, |AB| = 8.5 cm and |BC| = 5.65 cm. Find the length of its diagonals​

Answer 1

10.206 cm.

• The line segment joining the parallelogram's non-adjacent vertices is known as the diagonal. A parallelogram has two diagonals, and depending on the parameters and dimensions given, it is possible to determine the length of the diagonals using a variety of formulas.
• By connecting the parallelogram's two non-adjacent vertices, the diagonals of the parallelogram can be drawn. It should be observed that a parallelogram's two diagonals intersect one another, dividing it into congruent triangles.
• To get the length of the diagonals of a given parallelogram, apply the parallelogram diagonals formula. Various parallelogram types have different formulas.

Here, the area of the parallelogram ABCD is given as 40 cm².

Then, the area of a triangle = 20.

Now, semiperimeter s = $\frac{x+8.5+5.65}{2} =\frac{x+14.15}{2}$.

Then, we know that,

$\sqrt{s(s-8.5)(s-5.65)(s-x)} =20$.

This gives, the length of the diagonal = 10.206 cm.

Hence, the length of the diagonals are 10.206 cm.

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