Darren is making a map of population density in Central Florida. The two isosceles triangles below show the most and least populated areas according to Darren's results. The base of the large triangle covers 96 miles and the base of the small triangle covers 24 miles.
If the two triangles are similar and the length of the leg of the small triangle covers 31 miles, what is the distance, in miles, covered by m on Darren's map?
base of large triangle is to base of small triangle as 96 miles is to 31 miles.
base of large triangle is to base of small triangle as leg (m) of large triangle is to leg (31) of small triangle
Does this help?
74
To find the distance covered by m on Darren's map, we need to determine the scale factor between the small and large triangles.
The scale factor is the ratio of any corresponding side lengths in the two triangles.
In this case, we are given that the base of the small triangle is 24 miles, and the base of the large triangle is 96 miles.
So, the scale factor is:
Scale factor = (Base of large triangle) / (Base of small triangle)
= 96 miles / 24 miles
= 4
This means that any side length on the small triangle is 1/4th the length of the corresponding side on the large triangle.
Now, we are given that the length of the leg of the small triangle covers 31 miles.
So, the corresponding length on the large triangle can be found by multiplying the small length by the scale factor:
Length on large triangle = (Length on small triangle) * (Scale factor)
= 31 miles * 4
= 124 miles
Therefore, the distance covered by m on Darren's map is 124 miles.