Question

$△$ABC is drawn with the length of side AB being 4.8 cm. If $\angle$B is 35${}^{\circ }$ and $\angle$C is 65${}^{\circ }$, then, the perimeter of this triangle is

• A. 19.8 cm
• B. 18.2 cm
• C. 20.4 cm
• D. 21.1 cm

Answer 1

The correct option is C

20.4 cm

Here, we are given the measures of $\angle$B 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 A.

$\angle$A = 180${}^{\circ }$ - ( $\angle$B + $\angle$C ) = 180${}^{\circ }$ - ( 35${}^{\circ }$ + 65${}^{\circ }$ ) = 80${}^{\circ }$

Now, we have the following:

Length of side AB = 4.8 cm, measure of angle A = 80${}^{\circ }$ and measure of angle B = 35${}^{\circ }$

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 4.8 cm.

Step 2:
Measure the angle A with your protractor. Make a mark at 80 degrees and draw a line from A passing through the mark.

Step 3:
Measure the angle B with your protractor. Make a mark at 35 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 6.2 cm and the length of side BC is 8.1 cm

Hence perimeter of $△$ABC = AB + BC + AC = 6.2 cm + 8.1 cm + 4.8 cm = 19.1 cm