Question

$△$ABC is drawn with the length of side AB being 5 cm. If $\angle$A is 55${}^{\circ }$ and $\angle$C is 75${}^{\circ }$, then the perimeter of this triangle is

• A. 11 cm
• B. 12.8 cm
• C. 13.2 cm
• D. 14 cm

Answer 1

The correct option is C

13.2 cm

Here we are given the measures $\angle$A and $\angle$C.

We know that the sum of all the angles of a triangle is 180${}^{\circ }$. Hence we can find the measure of angle B.

$\angle$B = 180${}^{\circ }$ - ( $\angle$A + $\angle$C ) = 180${}^{\circ }$ - ( 55${}^{\circ }$ + 75${}^{\circ }$ ) = 50${}^{\circ }$

Now, we have the following:

Length of side AB = 5 cm, measure of angle A = 55${}^{\circ }$ and measure of angle B = 50${}^{\circ }$

With these information in hand, it is possible to construct a triangle, as explained below.

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

Step 2:
Measure the angle A with your protractor. Make a mark at 55 degrees and draw a line from A passing through the mark.

Step 3:
Measure the angle B with your protractor. Make a mark at 50 degrees and draw a line from B passing through the mark.

Step 4:
Name the point of intersection of these two lines as C and the $△$ABC is complete, as shown below.

Now, from the above construction, we see that the length of side AC is 4 cm and the length of side BC is 4.2 cm

Hence perimeter of $△$ABC = AB + BC + AC = 5 cm + 4.2 cm + 4 cm = 13.2 cm