Question

$△$XYZ is constructed such that XY = 2.5 cm, XZ = 5 cm and $\angle$X = 65${}^{\circ }$. Then $△$ABC is

• A. an obtuse scalene triangle
• B. an acute isosceles triangle
• C. an acute scalene triangle
• D. a right scalene triangle

Answer 1

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 $\angle$Y is 85${}^{\circ }$, measure of $\angle$Z is 30${}^{\circ }$ 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.