Answer:
The perimeter of QRS is 137.5
Step-by-step explanation:
From the given interval angles, we can see that the two triangles are congruent
so it is expected that the ratios of their corresponding sides are equal
this is because; 83 + 53 + 44 = 180
Now, let us work with the side facing the angle marked 53 in both triangles
For the smaller, we have the measure as 16
for the bigger, we have the measure as 44
So the scale factor here is 44/16 = 11/4 = 2.75
We have to multiply the measure of the sides of the smaller triangle by 2.75 to get that of the bigger triangle
in similar vein, we have to multiply the perimeter we have in the smaller triangle by 2.75 to get that of the bigger triangle
The perimeter of the smaller would be the sum of the side lengths
we have this as;
14 + 20 + 16 = 50
So the perimeter of the bigger triangle would be;
2.75 * 50 = 137.5
