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MAXImum [283]
3 years ago
14

On a map, the distance between two historical markers is 4.5 inches, and 2.5 inches represents 10 miles.

Mathematics
2 answers:
Morgarella [4.7K]3 years ago
7 0

Answer:

The actual distance between the historical markers is 18 miles.

Step-by-step explanation:

Given : On a map, the distance between two historical markers is 4.5 inches, and 2.5 inches represents 10 miles.  

To find : What is the actual distance between the historical markers?

Solution :

We have given that,

2.5 inches represents 10 miles.

i.e, 1 inch represent \frac{10}{2.5} miles.

1 inch = 4 miles.

Now, The distance between two historical markers is 4.5 inches.

The actual distance between the historical markers in 4.5 inch is

4.5 \text{ inch}=4.5\times 4\text{ miles}

4.5 \text{ inch}=18\text{ miles}

Therefore, The actual distance between the historical markers is 18 miles.

horsena [70]3 years ago
4 0
2.5 inches represents 10 miles.
Then 1 inch represents:
10 : 2.5 = 4 miles.
4.5   x  4  = 18 miles
Answer: The actual distance between the historical markers is 18 miles.
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check the picture below.

now, we're assuming the trapezoid is an isosceles trapezoid, namely AD = BC, and therefore the triangles are twins.

incidentally, b is the height of the trapezoid and likewise is also the altitude or height of the concrete triangle.

so we can simply get the area o the trapezoid, notice the bottom base is a+185+a, and then get the area of the concrete triangle and subtract the triangle from the trapezoid, what's leftover is just the vegetation area.

\bf \begin{cases} a=283\cdot cos(80^o)\\ a\approx 49.14\\ --------\\ b=283\cdot sin(80^o)\\ b\approx 278.70 \end{cases}\\\\ -------------------------------\\\\ \textit{area of a trapezoid}\\\\ A=\cfrac{h(x+y)}{2}~~ \begin{cases} x,y=\stackrel{bases}{parallel~sides}\\ h=height\\ ----------\\ x=185\\ y\approx \stackrel{a+185+a}{283.28}\\ h\approx\stackrel{b}{278.70} \end{cases} \\\\\\ A=\cfrac{278.70(185+283.28)}{2}\implies A\approx 65254.818

so that's the area of the trapezoid, now let's get the area of the triangle.

\bf \stackrel{triangle}{\cfrac{1}{2}(185)(b)}\implies \cfrac{1}{2}(185)(278.70)\qquad \approx 25779.80\\\\ -------------------------------\\\\ \stackrel{\textit{area for vegetation}}{\stackrel{\textit{area of trapezoid}}{65254.818}~~-~~\stackrel{\textit{area of triangle}}{25779.80}}\implies 39475.018

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