Question

N the figure, 2004-02-04-06-00_files/i0250000.jpg. If the ratio of the perimeter of to that of is 3:2 and the sum of the perimeters of the two triangles is 110, find the perimeter of each triangle.

A.
perimeter of = 66
perimeter of = 44
B.
perimeter of = 73
perimeter of = 37
C.
perimeter of = 37
perimeter of = 73
D.
perimeter of = 44
perimeter of = 66

Answer 1

Perimeter of triangle 1 = p1 = 66

Perimeter of triangle 2 = p2 = 44

Answer 2

I assume you needed to add the diagram. However, I'll assume that we have triangle 1 and triangle 2 and solve the problem.
You can then follow the same steps on the triangles you have.
Let perimeter of triangle 1 be p1 and that of triangle 2 be p2

First, we know that the ratio between p1 : p2 is 3:2, this means that:
p1/p2 = 3/2
p1 = (3/2) p2 .............> equation I

We also know that the sum of perimeters is 110, this means that:
p1 + p2 = 110 .........> equation II

Substitute by equation I in equation II as follows:
(3/2) p2 + p2 = 110
(5/2) p2 = 110
p2 = 44

Substitute by p2 in equation I to get p1 as follows:
p1 = (3/2) (44) = 66

Therefore:
perimeter of triangle 1 = p1 = 66
perimeter of triangle 2 = p2 = 44