Find the height of an acute triangle if area of the triangle is 49unit2 and the base of this triangle is twice the height of the triangle.
A
28 unit
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B
21 unit
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C
14 unit
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D
7 unit
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Solution
The correct option is D 7 unit Given,
Area of the triangle =49unit2 ⇒ Let, the height of a triangle be AD=h
Given: The base of a △ ABC is twice the height of the traingle. ⇒ The base of a triangle is BC=2h.
Let's consider a triangle ΔABC as shown.
Here BC=2h and AD=h
As we know,
Area of△ABC=12×BC×AD
49=12×2h×h
49=h×h
h2=49
h=√4=√7×7=7unit
Hence, the height of a triangle is 7 unit.
Option (d) is correct.