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Vika [28.1K]
3 years ago
13

The sign shows distances from a rest stop to the exits for different towns along a straight section of highway. The state depart

ment of transportation is planning to build a new exit to Freestone at the midpoint of the exits for Roseville and Edgewood. When the new exit is built, what will be the distance from the exit for Midtown to the exit for Freestone?
Midtown 17 mi.
Roseville 33 mi.
Edgewood 55 mi.
vertze vertze


When the new exit is built the distance from the exit for Midtown to the exit for Freestone will be miles.

Mathematics
1 answer:
torisob [31]3 years ago
3 0
Refer to the diagram shown below.

The exit for Freestone is built midway between Roseville and Edgewood,
therefore the distance from O to the new exit is
(1/2)*(33+55) = 44 mi.

Let x =  distance from Midtown to the new exit.
Because the distance from O to the new exit is equal to (x + 17), therefore
x + 17 = 44
x = 44 - 17 = 27 mi.

Answer:
When the new exit is built, the distance from the exit for Midtown to the exit for Freestone will be 27 miles.

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A right triangle has an area of 18 The length of each leg is 6 inches. If the triangle is not an isosceles triangle, what are al
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Given:

Area of a right triangle = 18 sq. inches

Length of one leg = 6 inches

To find:

The length of another leg.

Solution:

We know that, the area of a triangle is

A=\dfrac{1}{2}\times base\times height

In a right angle triangle, the area of the triangle is

A=\dfrac{1}{2}\times leg_1\times leg_2

Putting A=18 and leg_1=6, we get

18=\dfrac{1}{2}\times 6\times leg_2

18=3\times leg_2

Divide both sides by 3.

\dfrac{18}{3}=leg_2

6=leg_2

Both legs are equal so the given triangle is an isosceles right triangle.

If the triangle is not isosceles triangle, then the length of legs are factors of 36 because half of 36 is 18.

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Right triangle ABC is similar to triangle XYZ. If the length of side AB is 20.8 units, the length of side BC is 36.4 units, and
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Answer:

XY is 4 units.              

Step-by-step explanation:

We are given the following in the question:

Right triangle ABC is similar to triangle XYZ.

AB = 20.8 units

BC = 36.4 units

YZ = 7 units

We have to find the length of side XY.

Since the given triangles are similar, they have the following property:

The ratio of corresponding sides of similar triangles are equal.

We can write,

\displaystyle\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}

Putting the given values, we have,

\displaystyle\frac{AB}{XY}=\frac{BC}{YZ}\\\\\frac{20.8}{XY}=\frac{36.4}{7}\\\\XY = \frac{20.8\times 7}{36.4} =4 \text{ units}

Thus, the length of XY is 4 units.

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