Answer:
a) Height = OC = 13.3cm
b) Perimeter = 48.4cm
Step-by-step explanation:
a) Given:
ODC is a right angle triangle and
ABCD is part of it.
AB = 6 cm
CD = 15 cm
BC = 8 cm
∠BCD = 90 degrees
AB is parallel to DC
Find attached the diagram obtained from the given information.
From the diagram, ∆OAB is similar to ∆ODC.
∠OBA = ∠OCD = 90 degrees
To find the height, we would apply the similar triangles theorem.
The ratio of corresponding sides are equal and the angles are congruent.
OB/BA = OC/CD
OC = OB+BC = OB+8
OB/6 = (OB+8)/15
15OB = 6(OB+8)
15OB = 6OB + 48
9OB = 48
OB = 48/9 = 16/3
OC = 16/3 + 8
OC = 13⅓ cm = 13.3cm
Height = OC = 13.3cm
b) To get perimeter, we have to first determine OD (the hypotenuse of ∆OCD) as it is a right angled triangle
Using Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
OD² = OC² + CD²
OD² = (13⅓)² + 15²
OD² = 1600/9 + 225 = 3625/9
OD = √(3625/9)
OD = 20.1
Perimeter of ∆ODC= OC + CD + OD
= 13.3 + 15 + 20.1
Perimeter = 48.4cm
