The perimeter of the quadrilateral is 34cm. The diagonal divides the quadrilateral into 2 triangles, the perimeters
| December 5, 2020 | education
The perimeter of the quadrilateral is 34cm. The diagonal divides the quadrilateral into 2 triangles, the perimeters of which are 20cm and 26cm. Find the length of the diagonal.
denote the sides of the quadrangle as a, b, c and d cm
the length of the diagonal is x cm
since perimeter = 34, then a + b + c + d = 34
perimeters of triangles a + b + x = 20, c + d + x = 26
add these two expressions
a + b + c + d + 2x = 46
subtract the first
2x = 46 – 34 = 12
x = 6
Answer: 6 cm
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