The value of the ratio of perimeters of two similar figures is equal to the value of the ratio of their corresponding side lengths.
B
The value of the ratio of areas of two similar figures is equal to the square of the value of the ratio of their corresponding side lengths.
A
3240 yards
B
Grassland, see solution.
Practice makes perfect
We are told that two similar triangular regions are prepared for development.
We want to find the cost to surround the forest with a fence. Remember that when two figures are
similar, the value of the ratio of their perimeters is equal to the value of the ratio of their corresponding side lengths.
P_1/P_2=H/h
In this case, P_1 is the perimeter of the grassland, P_2 describes the perimeter of the forest, H represents the height of the grassland, and h indicates the height of the forest. Let's substitute P_1= 240, H= 60 and h= 45 into the equation and solve for P_2.
The perimeter of the forest region is 180 yards. We are told that it costs 6 dollars per foot to install fencing. To find the price to surround the forest with a fence, we need to convert the perimeter from yards to feet by multiplying 180 by 3.
180 yards * 3 feet/1 yard = 540 feet
Finally, let's multiply this by 6 to get the cost to surround the forest with a fence.
540 feet * 6 dollars/1 feet = 3240 dollars
It would cost $3240 to build a fence around the forest region.
We know that the cost to prepare 1 square yard of grassland is 15 dollars and the cost to prepare 1 square yard of forest is 25 dollars. We want to determine which region is more expensive to prepare. Let's find the ratio of the areas of the similar figures.
A_1/A_2=(H/h )^2
In this case, A_1 is the area of the grassland, A_2 describes the area of the forest, H represents the height of the grassland, and h indicates the height of the forest. Let's substitute A_1= 2400, H= 60 and h= 45 into the above equation and solve it for A_2.
The area of the forest is 1350 square yards. We can calculate the cost to prepare the forest region by multiplying 1350 by 25.
Forest Cost=1350 * $ 25 = $ 33 750
Next, we can find the cost to prepare the grassland region by multiplying 2400 by 15.
Grassland Cost= 2400 * $ 15 = $ 36 000
As we can see, it will cost more to prepare the grassland than the forest.
$ 36 000 &> $ 33 750
Grassland &> Forest
