Question

A triangle of sides AB = 5 cm, BC = 4 cm and AC = 3 cm is constructed. Then $△$ABC is

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

Answer 1

The correct option is B

a right scalene triangle

Let us construct the required triangle as follows:

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

Step 2:
Use your compass to make a circle with centre at point A and the radius 3 cm.

Step 3:
Use your compass to make a circle with centre at point B and the radius 4 cm.

Step 4:
In the point of intersection between the two circles, you'll find the point C.
Complete the triangle by drawing the lines between all three points, as shown below.

Now, by above construction, we see that the measure of $\angle$C is 90${}^{\circ }$, measure of $\angle$A is 37${}^{\circ }$ and measure of $\angle$B is 53${}^{\circ }$.

Hence the given triangle is a right-angled scalene triangle.

Hence option (b) is the correct one.