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Ivanshal [37]
2 years ago
9

Can anyone give a step-by-step guide on how to answer these types of questions? I'm really struggling with similar shapes so tha

nk you in advance.

Mathematics
2 answers:
Dafna11 [192]2 years ago
8 0

Answer:

a) 8cm

b) 19.8cm

Step-by-step explanation:

The key to these types of questions is to keep proportions in mind.

To solve the first question, you want to find the proportion of the smaller triangle to the bigger triangle. The length of AE is 6cm, but the length of AD is (6+4) = 10cm. So the proportion of the bigger triangle to the smaller triangle is 10/6. So to find the lengths of the sides of the bigger triangle, we want to keep this number in mind.

The BE side is parallel to CD, so we have to use length of BE multiplied by the proportion in order to get the length of CD.

CD = 4.8 * (10/6) = 8

CD = 8cm

For the second question, you use the same concept to find all the other side lengths. The only one you need left for the shape EBCD is side BC. Do the same thing you did before, take the length of the side of the smaller triangle that corresponds with side AC on the bigger triangle. In this case, it's AB, which is 4.5cm. Multiply this by 10/6 to get AC.

AC = 4.5 * (10/6) = 7.5

AC = 7.5

But we're not done. We just found the length of AC, but we need the length of BC to calculate the perimeter. To do this, we want to take the length of AC - the length of AB.

7.5 - 4.5 = 3

So the length of BC is 3cm. Now, to find the perimeter, just add all the sides of EBCD together.

4.8 + 4 + 8 + 3 = 19.8cm.

Hope this helps.

sergeinik [125]2 years ago
4 0

Answer:

a) CD = 8 cm

b) Perimeter of EBCD is 19.8 centimeters

Step-by-step explanation:

For this question, you can assume that ΔABE and ΔACD are similar. That's proven by BE ║ CD, but that's not directly relevant to the question so I won't explain it unless you would like me to.

In 2 similar triangles, all corresponding angles are congruent and all corresponding sides have the same scale factor.

For example, in ΔABC and ΔXYZ:

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

Using those relationships, you can solve for any side in one triangle given the corresponding side in the other triangle.

A)

In the given triangles ΔABE and ΔACD, CD corresponds to BE, so:

\frac{CD}{BE} =\frac{AD}{AE}

where AD is just 6 + 4 = 10.

\frac{CD}{4.8} =\frac{10}{6} \\\\\frac{CD}{4.8} =1.6667\\\\CD=8

CD = 8cm

B)

Doing the same thing as above, now find the length of AC:

\frac{AC}{AB} =\frac{AD}{AE} \\\\\frac{AC}{4.5} =\frac{10}{6}\\\\\frac{AC}{4.5} =1.6667\\\\AC=7.5

Now, to find BC:

BC=AC-AB\\BC=7.5-4.5\\BC=3

Finally, add up the sides to find the perimeter of EBCD:

4.8+3+8+4\\19.8

Perimeter of EBCD is 19.8 centimeters

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Galina-37 [17]

<u>Answer:</u>

x + y ≥ 26 + 15

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Step-by-step explanation:

First, write an equation to represent the total cost to wash cars:

$5x = cost for cars

Then, write another for trucks:

$8y = cost for trucks

If the question is saying that they will wash at least 26 cars and 15 trucks, that means they could wash more. This means that we'll need an inequality:

This inequality represents that the total number of cars and trucks they wash will be at least—which means that it is equal to or greater than—than the amount given:

x + y ≥ 26 + 15

Any equation or inequality with two unknowns is not solvable, meaning we need a system of equations:

If they make at least $250, that means that we need to combine the costs of the cars and trucks to make an inequality:

5x + 8y ≥ 250

Now you have your system of equations:

x + y ≥ 26 + 15

5x + 8y ≥ 250

8 0
3 years ago
The angle of elevation of the top of a tower from a point 100m away is 45 degrees. What is the height of the tower to the neares
OLEGan [10]
<h3>Answer: 100 meters</h3>

===========================================

Explanation:

If you draw out the diagram, then you'll find that a 45-45-90 triangle forms. The nice thing about this type of triangle is that the two legs are always the same length. The horizontal leg is 100 meters, so the vertical leg must also be 100 meters.

Side note: this type of triangle is an isosceles right triangle.

---------

You could use the tangent rule to get the same thing

tan(angle) = opposite/adjacent

tan(45) = 100/x

1 = 100/x

1*x = 100

x = 100

In this case, the opposite leg is the vertical leg since it is furthest from the angle of elevation.

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3 years ago
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Answer:

Step-by-step explanation:

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2 years ago
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stiv31 [10]

Answer:

MG=56\ units

Step-by-step explanation:

step 1

Find the value of x

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem we have that

∆EGF~∆EML

so

\frac{EG}{EM}=\frac{EF}{EL}

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Answer:

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