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Question

ABC is constructed such that AB = 4 cm, BC = 4.5 cm and A = 30. Then the length of side AC is


A

6.3 cm

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B

8.4 cm

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C

5.5 cm

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D

7.5 cm

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Solution

The correct option is D

7.5 cm


Step 1:
Draw the base line AB of the length 4 cm.

Step 2:
Measure the angle A with your protractor. Make a mark at 30 degrees and draw a line from A passing through the mark.

Now we must locate C. It should be 4.5 centimetres from B and also should be on the upper line, in order to form the required triangle. All points at a distance of 4.5 cms from B are on the circle centered at B of radius 4.5 cm. Thus we have the next step.

Step 3:
Draw a circle with centre at B and radius 4.5 cm. The point at which this circle cuts the line through A is the required point C.

Thus ABC is formed.

From the above construction, we see that the length of side AC is 7.5 cm.


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