Answer:
i. The ratio of the areas of the two triangles is 5:8.
ii. The area of the larger triangle is 24 in².
Step-by-step explanation:
Let the area of the smaller triangle be represented by  , and that of the larger triangle by
, and that of the larger triangle by  .
.
Area of a triangle =  x b x h
 x b x h
Where; b is its base and h the height.
Thus,
a. The ratio of the area of the two triangles is:

Area of smaller triangle =  x b x h
 x b x h
                                        =  x 5 x h
 x 5 x h
                                        =  h
h
Area of the lager triangle =  x b x h
 x b x h
                                            =  x 8 x h
 x 8 x h
                                            = 4h
So that;
Ratio = 
          = 
The ratio of the areas of the two triangles is 5:8.
b. If the area of the smaller triangle is 15 in², then the area of the larger triangle can be determined as;
 =
 = 
 =
 = 
5  = 15 x 8
 = 15 x 8
        = 120
 =
 = 
     = 24 
The area of the larger triangle is 24 in².