Question 1227: this refers to similar figures. I need to know the ratio of perimeters and areas of the scale factor 1:4, and r:2s, and i need to know the raiot of areas and the scale factors of ther ratio of perimeters 3:13, and using the ratio of areas 9:64 i need to know ratio of perimeters and the scale factors. Then my next question is this, L, M, and N aare the midpoints of the sides of triangle ABC. Find the ratio of the perimeters and the ratio of the areas of triangle LMN and triangle ABC.
Also, A quadrilateral with sides 8 cm, 9 cm, 6cm, and 5cm, has and area of 45cm2. Find the area of similar quadrilateral whose longest side is 15cm.
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Sol: Since the perimeter is of one dimension, and the area is of two dimension.
The main idea of this question is "Between tow similar figures,the ratio of areas is the
square of the ratio of perimeters." I am not sure what you mean about scale factor ,but I think
it is the ratio of sides and so it is the same as the ratio of perimeters.
If ratio of area is 1:4, then the ratio of the perimeters is 1:2 (scale factor is 1/2 I guess)
If the scale factors of their ratio of perimeters 3:13, then the ratio of areas is 9:169
If ratio of area is 9:64, then the ratio of the perimeters is 3:8
[By the way, thewriting and meaning of your first part is not clear to me(unclear grammar).
So, you have to figure out by yourselfand answer the missing scale factors.]
Triangle LMN is similar to triangle ABC, their the ratio of the perimeters is 1:2 and the
ratio of the areas is 1:4.
Let the area of similar quadrilateral whose longest side is 15cm is D cm^2, the ratio of the two longest sides is 9:15 =3:5 and
45 : D = 3^2: 5^2 = 9: 25, hence D = 45*25/9 = 125 cm^2
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