Question

A triangle XYZ is constructed such that XY = 2.5 cm, XZ = 5 cm and angle X = 65 degrees. Then triangle ABC is a/an _____.

• A. Acute angled scalene triangle
• B. Acute angled isosceles triangle
• C. Right angled triangle
• D. Equilateral triangle

Answer 1

The correct option is A Acute angled 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 angle Y is 85 degrees, measure of angle Z is 30 degrees and the length of side YZ is 4.6 cm.

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