Question

In the diagram, ABCD is a part of a right angle triangle ODC. If AB = 6 cm, CD = 15 cm, BC = 8 cm angle BCD = 90 degrees and AB is parallel to DC, calculate, correct to 1 decimal place, the: (a) height (b) perimeter, of the triangle ODC

Answer 1

• a. The height of triangle ODC is 11.25 cm.
• b. The perimeter is 40 cm.

Step-by-step explanation:

To calculate the height and perimeter of triangle ODC, we can use the properties of similar triangles and the Pythagorean theorem.

(a) To find the height, we can use the fact that AB is parallel to DC. This means that triangle ABC and triangle ODC are similar triangles. The ratio of corresponding sides in similar triangles is equal. We can set up the following proportion:

AB/BC = OD/DC

Substituting the given values, we have:

6/8 = OD/15

Cross-multiplying, we get:

8 * OD = 6 * 15

Simplifying, we have:

8OD = 90

Dividing both sides by 8, we get:

OD = 11.25 cm

So, the height of triangle ODC is 11.25 cm.

(b) To find the perimeter of triangle ODC, we can use the Pythagorean theorem. In triangle ODC, OD is the hypotenuse and BC and CD are the other two sides.

Using the Pythagorean theorem, we have:

OD² = BC² + CD²

Substituting the given values, we have:

OD^2 = 8² + 15²

Calculating, we get:

OD² = 64 + 225

OD² = 289

Taking the square root of both sides, we get:

OD = 17 cm

The perimeter of triangle ODC is equal to the sum of the lengths of its sides. So, the perimeter is:

Perimeter = OD + BC + CD = 17 + 8 + 15 = 40 cm

Therefore, the height of triangle ODC is 11.25 cm and the perimeter is 40 cm.

Answer 2

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