Question

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Question no. 64!
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Answer 1

Given:

AB = 10 cm

BC = 20 cm

To FInd:

The length BD

Explanation

The area of the triangle can be found in 2 ways:

(1) Base = BC and Height = AB

(2) Base = AC and Height = DB

Solution

Find length AC:

a² + b² = c²

c²  = 10²  + 20²

c²  = 100 + 400

c²  = 500

c = 10√5

Find the area of triangle ABC:

Area = 1/2 x base x height

Area = 1/2 x 10 x 20

Area = 100 cm²

Find the length BD:

Area = 1/2 x base x height

1/2 x AC x BD = 100

1/2 x 10√5 x BD = 100

5√5 x BD = 100

BD = 100 ÷ 5√5

BD = 4√5 cm

Answer: (2) 4√5