Answer:
DB = 9 in , AB = 9 in , AD = 10 in
Explanation:
* Lets explain how to solve the problem
- The figure ABCD is a parallelogram
- The altitude from B to the side AD bisects it
- In Δ DAB
∵ BE ⊥ AD where E is the point of intersection between the
altitude from point B to the side AD
∵ The altitude from point B to the side AD bisects it
∴ Point E is the mid-point of AD
- In any triangle if a segment drawn from a vertex perpendicular
and bisects the opposite side, then the triangle is isosceles triangle
∵ BE ⊥ AD and EA = ED
∴ Δ BAD is an isosceles triangle
∴ AB = DB
- The perimeter of the parallelogram is 38 inches
∴ 2 AD + 2 AB = 38 ⇒ divide both sides by 2
∴ AD + AB = 19
- The perimeter of Δ BAD is 10 less
∴ The perimeter of Δ BAD = 38 - 10 = 28
∴ AB + DB + AD = 28
∵ AB + AD = 19
∴ 19 + DB = 28 ⇒ subtract 19 from both sides
∴ DB = 9
∵ AB = DB
∴ AB = 9
∵ AB + AD = 19
∴ 9 + AD = 19 ⇒ subtract 9 from both sides
∴ AD = 10
∴ DB = 9 in , AB = 9 in , AD = 10 in