Question

choose similar polygons have areas of 128 in2 and 98 in 2. if the smaller polygon has a perimeter of 42 inches what is the perimeter of the larger polygon 

Answer 1

Let the smaller polygon have side lengths a and the larger polygon have side lengths b. Since the polygons are similar, the ratio of corresponding side lengths is the same as the ratio of their areas. That is:

b^2 / a^2 = 128 / 98

Simplifying this expression, we get:

b / a = √(128 / 98) = √(64 / 49) = (8 / 7)

Now we can use the fact that the perimeter of the smaller polygon is 42 inches:

4a = 42

a = 10.5

Substituting this into the ratio we found above, we get:

b = (8 / 7) * a = (8 / 7) * 10.5 = 12

Therefore, the larger polygon has a perimeter of:

4b = 4 * 12 = 48 inches.