A triangle is enlarged by a scale factor of 10/3.
a) If the perimeter of the copy is 36 meters, find the perimeter of the original triangle using the proportion 10/3.
b) If the area of the copied triangle is 48 meters squared, use a proportion to find the area of the original triangle.
Please HELP me! I don't really know how I can solve this...
( copy/ orginal) = 10/3
(10/3)=(copy perimeter)/(orig.perimeter)
(10/3)=(36/X)
cross multiply and you get
10x=108 then x= 10 4/5 =10.8
x=perimeter of org.
triangle
Do the same with part b but this time it's area.
(10/3)=(48/x) ===> x= 14 2/5 =14.4
Samantha, your second part is not correct
The area of similar figures is proportional to the square of their sides. Since perimeter is a function of the sides you last line should have been
(10/3)2 =(48/x) ===> x= 4.32
To solve these problems, you can use the fact that the ratio of corresponding sides of similar figures is equal to the scale factor.
a) Let's say the perimeter of the original triangle is P. According to the problem, the scale factor is 10/3. This means that the ratio of the perimeters of the copy to the original is also 10/3. We can set up the following proportion:
(Perimeter of copy) / (Perimeter of original) = (Scale factor)
Plugging in the given values, we get:
36 / P = 10/3
To solve for P, we can cross multiply:
36 * 3 = 10P
108 = 10P
Dividing by 10, we find:
P = 108 / 10 = 10.8
Therefore, the perimeter of the original triangle is 10.8 meters.
b) Let's say the area of the original triangle is A. The area of a triangle is proportional to the square of the length of its sides. Since the scale factor is 10/3, the ratio of the areas of the copy to the original is equal to the square of the scale factor, (10/3)^2.
We can set up the following proportion:
(Area of copy) / (Area of original) = (Scale factor)^2
Plugging in the given values, we get:
48 / A = (10/3)^2
To solve for A, we can cross multiply:
48 * (3^2) = 10^2 * A
48 * 9 = 100 * A
Dividing by 100, we find:
A = (48 * 9) / 100 = 4.32
Therefore, the area of the original triangle is 4.32 square meters.