Question 1180868: the area of two similar polygons are 64sq. units and 100sq. units respectively. if a side of the larger polygon is 36 units find the corresponding sides of the smaller polygon
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the ratio of the areas is the square of the ratio of the sides.
if the area of the smaller polygon is 64 and the area of the larger polygon is 100, then the ratio of the area of the larger polygon to the ratio of the area of the smaller polygon is 100/64 = 1.5625 and the ratio of the corresponding sides if sqrt(100) / sqrt(64) = sqrt(100/64) = 1.25.
note that sqrt(100) / sqrt(64) = 10/8 = 1.25.
if the polygons were squares, then the polygon with an area of 100 has a side of 10 and the polygon with an area of 64 has a side of 8 and the ratio of the corresponding sides is 10/8 = 1.25.
it the polygons were rectangles, than the polygon with an area of 100 could have length of 20 and width of 5 where 20 * 5 = 100 square.
the length would be equal to 4 times the width.
to find the comparable length with an area of 64, the formula would be:
L * W = 64
L = 4 * W
4*W * W = 64
4*W^2 = 64
W^2 = 64/4 = 16
W = 4
L = 4*W = 16
the length of the smaller rectangle would be 16 and the width = 4.
the ratio of corresponding sides would be 20/16 and 5/4.
the ratios would be 1.25 and 1.25 respecitvely.
the formula holds true.
if the ratio of the areas is 100/64, then the ratio of the corresponding sides if sqrt(100) / sqrt(64) = 10/8 = 1.25.
here's a reference.
https://mathbitsnotebook.com/Geometry/Similarity/SMArea.html#:~:text=If%20two%20polygons%20are%20similar%2C%20the%20ratio%20of%20their%20areas,ratio%20of%20their%20corresponding%20sides.&text=If%20two%20solids%20are%20similar,ratio%20of%20their%20corresponding%20sides.
|
|
|
