# The two sides of the quadrilateral are 1 and 7. One of the diagonals, which is 3 in length, divides

March 31, 2021 | education

| **The two sides of the quadrilateral are 1 and 7. One of the diagonals, which is 3 in length, divides it into two isosceles triangles. What is the perimeter of this quadrilateral?**

Let us consider how a diagonal of 3 cm and sides of 1 cm and 7 cm can be distributed among themselves.There cannot be such a triangle with sides 1, 3 and 7, since the condition of sides (1 + 3)> 7 is not satisfied, which means that the diagonal equal to 3 connects two triangles with sides of 1; 1 & 3 & 7; 7; and 3. But there cannot be a triangle with sides 1, 1, 3, since the sum (1 + 1) <3, which means that a triangle with sides 1, 3, 3 is also isosceles, and the sides of the quadrangle are: 1, 3, 7 , 7, the perimeter of which is 18.

Answer: 18.

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