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Question

Construct an equilateral triangle whose altitude is 5 cm. Then, area of the required triangle is:

A
13.6 cm2
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B
14.5 cm2
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C
12.8 cm2
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D
11.2 cm2
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Solution

The correct option is D 14.5 cm2
We know that in an equilateral triangle, all angles are equal to =600 and the altitude bisects the opposite angle.
Hence, follow the steps given below to construct the triangle.
1. Draw a line PQ and mark a point D on it.
2. Construct a perpendicular of length DA=5cm to PQ at point D
3. Construct DAR=6002=300 to intersect PQ at B
4. Measure BD and cut off an arc on PQ of same distance DC on the other side of D
5. Join A to C
6. ABC is the required equilateral triangle.

On measuring the length of the sides, we get side length as 5.8 cm
Area of triangle =12×5.8×5=14.5 cm2

405566_187698_ans.jpg

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