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Question

XYZ is constructed such that XY = 5 cm, XZ = 8.5 cm and X = 75. Then XYZ is


A

an obtuse scalene triangle

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B

an acute isosceles triangle

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C

a right scalene triangle

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D

an acute scalene triangle

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Solution

The correct option is D

an acute scalene triangle


Step 1:
Draw the base line XY of the length 5 cm.

Step 2:
Measure the angle X with your protractor. Make a mark at 75 degrees and draw a line from X passing through the mark.

Step 3:
Cut an arc of radius 8.5 cm on the line passing through the point X. The point where this arc cuts the line is the point Z.

Step 4:
Draw a line from Y to point Z, to get the required triangle XYZ, as shown below.

From the above construction, we see that the measure of Y is 34, measure of Z is 71 and the length of side YZ is 8.7 cm.

Hence, the given triangle is an acute-angled scalene triangle.


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