Geometry homework help- ratios of similarity?

Question

Two figures have a ratio of similarity of 2:5
If the area of the larger is 100 square units, what is the area of the smaller?

My teacher told me the answer is sixteen, but I really need to know the process.

Any help in understandable terms would be GREATLY appreciated.

Answer 1

If your two figures have a ratio of similarity of 2:5, then each side of the smaller one is the side of the larger one times 2 and divided by 5. This might lead you to believe that your area would be 100 times 2 and divided by 5 = 40. This is, however, not the case. If each side is times 2 and divided by 5, the total area is times 2 times 2 divided by 5 divided by 5. = 16
The best way to imagine this problem is by assuming your shape is a square. How large is each side of the square if the area is 100 square units? Each side must be 10 units, since 10 times 10 is 100 square units. Now shrink each side by multiplying by 2 and dividing by 5. Each side is now 4 units long. How much area is your square? 4 times 4 is 16 square units!

Answer 2

I'm assuming, from the answer of sixteen, that the figure is a square. A ratio of similarity is a ratio between the sides of two similar figures. If the area of the larger square is 100 square units, then one side would be the square root of that, 10. Knowing the ratio will help you determine the length of one side of the smaller square because the ratio is the same for any length sides. Thus, 5/2 has to equal 10/x where x is the length of the unknown side. Using cross multiplication:
5x=20
x=4
If one side equals 4 then the area equals 4 squared or 16.

Answer 3

Ok here's what you need to do:
the ratio is 2:5 and the area of the larger unit is 100 square units that means it is 10^2 (10 squared). 2/5 = x/10 x is the unit value of the area that you want to find. Therefore now you have 5x = 20 and x = 4; but you need to square 4 because the answer needs to be given in square units thus; 4^2 = 16.

Answer 4

whenever you get into this kind of project, discover an a lot less puzzling problem and learn from it. enable's take 2 squares: one has aspects 2, the different has aspects 4, for a 2:a million ratio. What are the parts? properly, 2 x 2 = 4; 4 x 4 = 16. ration of two:a million ends up in area ratio of four:a million hmmmm how about 3 and four?? ratio of three:4 3 x 3 - 9 4 x 4 = 16. ratio of three:4 ends up in area ratio of 9 : 16 hmmmmm how about a triangle with base of four and altitude of three; vs base of 12 and altitude of 9? ratio - 3:a million area = a million/2 base x top 4/2 x 3 = 6; 12/2 x 9 = fifty 4 ratio of three:a million ends up in fifty 4/9 or 9:a million hmmmm Now, lessee 2:a million ==> 4:a million 3:4 ==> 9/16 3:a million ==> 9:a million i imagine I see a trend right here. Write in case you want better help. continuously, tony