# As a result of measuring the four sides and one diagonal of the quadrangle, the numbers 1 were obtained

As a result of measuring the four sides and one diagonal of the quadrangle, the numbers 1 were obtained; 2; 2.8; 5 and 7.5. What is the length of the measured diagonal?

A diagonal divides a quadrilateral into two triangles.

In each triangle, the sum of the two sides must be greater than the diagonal, and the difference is less than the diagonal.

The table shows all possible combinations of different diagonals and sides of triangles with a base-diagonal.

Only in one case (line 7) the condition for the length of the diagonal and the lengths of the sides of the triangles is satisfied.

Conclusion: A quadrilateral with a diagonal of 2.8 is possible.

Answer: The diagonal is 2.8 cm long.

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