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the two pentagons are similar what do you think that means?
I dont know how to start this problem.
the ratio of their perimeters is equal to the ratio of their corresponding side lengths
How do i find any of their side lengths though?
we have two figures A and B if A is similar to B it means that if we multiply A with some number x we will get B so Ax =B (THEY ARE IN RATIO) what does this mean to us side(A) * x = side(B) where side(A) means side of A perimeter(A)*x = perimeter(B) area of(A)*x = area(B) i hope you get the point
it is given that the Area of I = 43 cm^2 Area of II = 387 cm^2 but they are similar so find their ratio Area II/Area I = 387/43 = 9 the perimeter of II would be 3*25 = 75 cm and the side length of II would be 75/5 = 15cm
We know that if you find the ratio of the areas and take the square root, you will have the ratio of the perimeters So find the ratio of the areas: 387/43
dammit heather why are you so hot ? :X
why 3 X 25?
because the units of area is cm^2 and the units of perimeter is cm
9cm^2 = 3cm you cannot really multiply 25cm with 9cm^2 because their units are different so you have to convert 9cm^2 to 3cm before you can multiply them think about adding 10grams to 15 meters it does not make sense does it
oh yeah i think i get it so i can say.... perimeter II= 3/1 X 25? why am i multiplying 25 though... where did that come from?
25 is the perimeter of the small one you are trying to find the big one
yeah but why multiply the perimeter of the small one by the ratio of the areas of the two? What exactly is the formula?
there is no formula the two objects are similar which means they are in ratio so their areas are in ratio and their peremeters are in ratio and their sides aswell
bcuz the ratio tells you how big they are to each other they are 3:1 that means the bigger one is 3 times bigger then the smaller one so the perimeter of the big one is going to be 3 times bigger then the small one
does this make sense... Perimeter of II/Perimeter of I= 3/1 therefore, Perimeter of II= 3(25)=75 cm.
looks good to me :)
Thanks for the help guys!
this is how you answer it given : Ar(I) = 43cm^2 Ar(II) = 387cm^2 Perimeter(I) =25cm^2 to find: Perimeter(II) Since fig.I and fig.2 are similar it implies that the two objects are in ratio. Ar(II)/Ar(I) = 387cm^2/43cm^2 = 9cm^2 the magnitude of their ratio = 9 cm^2 or sqrt(9cm^2) = 3cm upon multiplying Perimeter(I) with 3 we get, 25*3 = 75cm^2 which is the perimeter of fig.II
No problem :)
well that will also work :X