Construct a parallelogram ABCD in which AB = 6.5 cm, AC = 3.4 cm and the altitude AL from A is 2.5 cm. Draw the altitude from C and measure it.

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3.5 cm

2.5 cm

4.5 cm

1.5 cm

answer is B.

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Detailed Solution

Given,
AB = 6.5 cm, AC = 3.4 cm and the altitude AL from A is 2.5 cm
For constructing a parallelogram, we have to follow the below steps:
(1) Draw a line DC = 6.5 cm as a base line. As we know that parallelograms have parallel lines of equal lengths. Here, we consider AB and DC are parallel lines of equal length.
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(2) Draw 2 arcs from points D and C with the help of a compass with radius 3.4 cm. Now from point D draw a line cutting arc and mark it as A and similarly draw a line from point C and mark it as B.
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(3) Now the construction of our parallelogram ABCD is completed.
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Now we need to find the measure of altitude CM with the help of compass and a ruler. We will get 2.5 cm.
We know that altitudes in parallelograms are parallel and equal. So, the altitude AL from A is 2.5 cm.
Therefore, measure of altitude CM = 2.5cm.
So, option (2) is correct for this question.

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