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Question 1199435: The linear scale factor of two similar shapes is 4:7.if the area of the bigger shape is 490cmsquare, what is the area of the smaller shape?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Consider a square with side 4 cm.
Then consider another square with side 7 cm.
The figures do not have to be squares. They can be any shape you want, as long as they are similar.
Squares just happen to be the easiest shape to work with in this case.
Any two squares are similar.
The ratio of the side lengths is 4:7, which is what it means to have this linear scale factor.
Now compute the areas
4^2 = 16
7^2 = 49
The ratio of the areas is 16:49
We can multiply both parts of this ratio by 10 to get 160:490
The 490 matches with the area of the larger shape, so the smaller shape is 160 square cm.
Alternatively you can solve this equation
16/49 = x/490
to find that x = 160
Answer:
160 square cm
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