Question

. For the triangle ABC, the base BC = 20 cm. AB = 15 cm, AC = 7 cm. Compute the height of the triangle AD. ​

Answer 1

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Answer 2

Given :-

• AB = 15cm.
• BC = 20cm.
• AC = 7cm.

To Find :-

• AD = ? (Height)

Solution :-

→ Semi - Perimeter of ∆ABC = (Perimeter)/2 = (20 + 15 + 7)/2 = 21 cm.

So,

→ Area of ∆ABC = √{s(s - a)(s - b)(s - c)} [ Heron's formula. ]

( a, b and c are sides of ∆. )

Putting all values we get,

→ Area = √{21 * (21 - 20)(21 - 15)(21 - 7)}

→ Area = √(21 * 6 * 14)

→ Area = √(3 * 7 * 3 * 2 * 2 * 7)

→ Area = √(2² * 3² * 7²)

→ Area = (2 * 3 * 7)

→ Area = 42 cm².

Now, we also know that,

→ Area of ∆ = (1/2) * Base * Height

Given base is 20cm.

Therefore,

→ (1/2) * 20 * Height = 42

→ 10 * Height = 42

dividing both sides by 10,

→ Height = 4.2 cm.

Hence, AD is Equal to 4.2 cm.

Learn More :-

1. In ∆ ABC, AD is a median. If AB = 8, AC = 15

and AD = 8.5, find BC.

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