Question

A triangle is constructed such that the length of its two sides are 7 cm and 2.5 cm and the angle opposite to the side of length 2.5 cm is 15${}^{\circ }$. This construction results in the formation of two triangles. Then the perimeter of the so formed obtuse angled triangle is

• A. 9.5 cm
• B. 11 cm
• C. 18 cm
• D. 20.5 cm

Answer 1

The correct option is C

18 cm

Step 1:
Draw the base line AB of the length 7 cm.

Step 2:
Measure the angle A with your protractor. Make a mark at 15 degrees and draw a line from A passing through the mark.

Now we must locate C. It should be 2.5 cm from B and also should be on the upper line, in order to form the required triangle. All points at a distance of 2.5 cm from B are on the circle centred at B of radius 2.5 cm. Thus, we have the next step.

Step 3:
Draw a circle with centre at B and radius 2.5 cm. This circle cuts the line through A at two points. Name the third vertex of the smaller triangle as $C_1$ and the third vertex of the bigger triangle as $C_2$.

From, the above construction we see that $\angle AB{C}_1$ is an acute angle and $\angle AB{C}_2$ is an obtuse angle.

We need to find the perimeter of the obtuse angled triangle and so we measure the length of side $A{C}_2$.

Length of side $A{C}_2$ = 8.5 cm

Therefore the perimeter of $△AB{C}_2$ = $AB+B{C}_2+A{C}_2$ = 7 cm + 2.5 cm + 8.5 cm = 18 cm.