The diagonal divides a quadrilateral with a perimeter of 34 dm into two triangles with perimeters of 24 dm
| September 24, 2021 | education
The diagonal divides a quadrilateral with a perimeter of 34 dm into two triangles with perimeters of 24 dm and 30 dm2. What is the length of the diagonal?
The perimeter of the quadrilateral is:
Ravsd = AB + BC + CD + AD = 34 cm.
The perimeter of the triangle ABC is:
Ravs = AB + BC + AC = 24 cm.
AC = 24 – AB – BC. (1).
The perimeter of the triangle ACD is equal to:
Dist = AD + CD + AC = 30 cm.
AC = 30 – AD – CD. (2).
Add equations 1 and 2.
AC + AC = 24 – AB – BC + 30 – AD – CD.
2 * AC = 54 – (AB + BC + CD + AD).
2 * AC = 54 – Ravsd = 54 – 34 = 20 cm.
AC = 20/2 = 10 cm.
Answer: The length of the diagonal is 10 cm.
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