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Question

Find the height of an acute triangle if area of the triangle is 49 unit2 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 =49 unit2
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=7 unit

Hence, the height of a triangle is 7 unit.
Option (d) is correct.

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