Question

angle a equal to 90 degree AD perpendicular to BC. if BD = 2 cm and CD equals to 8 cm.
find AD

Answer 1

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Answer 2

Answer:

AD = 4 cm

Step-by-step explanation:

Given: ∠A = 90° and AD is ⊥ to BC

           BC = 2 cm and CD = 8 cm

To find: AD

Figure is atttaced.

BC = BD = CD

BC = 2 + 8

BC = 10 cm

In ΔABC,

By Pythagoras Theorem

AB² + AC² = BC²

⇒ AB² + AC² = (10)²

⇒ AB² + AC² = 100 .................(1)

In Δ ABD,

By Pythagoras Theorem

AB² = AD² + BD²

⇒ AB² = AD² + 2²

⇒ AB² = AD² + 4 .........................(2)

In Δ ADC

By Pythagoras Theorem

AC² = AD² + CD²

⇒ AC² = AD² + 8²

⇒ AC² = AD² + 64.........................(3)

Add (2) and (3)

AB² + AC² = AD² + 4 + AD² + 64

AB² + AC² = 2AD² + 68 ..................(4)

From (1) & (4), we get

100 = 2AD² + 68

2AD² = 100 - 68

2AD² = 32

AD² = 16

AD = √16

AD = 4 cm

Therefore, AD = 4 cm