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Question

# △XYZ is constructed such that XY = 2.5 cm, XZ = 5 cm and ∠X = 65∘. Then △ABC is

A

an obtuse scalene triangle

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B

an acute isosceles triangle

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C

an acute scalene triangle

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D

a right scalene triangle

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Solution

## The correct option is C an acute scalene triangle Step 1: Draw the base line XY of the length 2.5 cm. Step 2: Measure the angle X with your protractor. Make a mark at 65 degrees and draw a line from X passing through the mark. Step 3: Cut an arc of radius 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 85∘, measure of ∠Z is 30∘ and the length of side YZ is 4.6 cm Hence the given triangle is an acute-angled scalene triangle. Hence option (c) is the correct one.

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