1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
Explain how you could find the number of cups in 5 gallons of water
jolli1 [7]
It take 80 cup to fill 5 gallons
4 0
3 years ago
Read 2 more answers
24 is 80% of what number
loris [4]
Write this as an equation and solve
.8x = 24 \\ x =  \frac{24}{.8}  = 30
The number is 30
6 0
3 years ago
Read 2 more answers
Two cubic meters of mercury have a mass of 27190 kilograms. What is the density of mercury?
garik1379 [7]

Answer:

27,190

Step-by-step explanation:

7 0
3 years ago
Tina had 1.84 liters of olive oil in a bottle. she added more olive oil and now has 2.67 liters.  how many liters of olive oil d
katovenus [111]
2.67 - 1.84 = 0.83
Tina added 0.83 liters of olive oil.
7 0
3 years ago
Solve the equation: 39=3m-12
mote1985 [20]

Answer:

Step-by-step explanation:

M=17

Hope this helps mark me as brainiest

3 0
2 years ago
Read 2 more answers
Other questions:
  • A nutrition laboratory tested 25 "reduced sodium" hotdogs of a certain brand, finding that the mean sodium content is 310 mg wit
    13·1 answer
  • 0.58333333333 as a whole number​
    5·1 answer
  • What is (-1 1/2) (-1 1/2)?
    7·2 answers
  • How do I find the length and the width?
    11·2 answers
  • The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the bridge is 1210 m long and
    12·1 answer
  • Charles bought 24 blow-pops for $7.20. His little sister Tracy wants 11 blow-pops. How much will 11 blow-pops cost?
    15·1 answer
  • the latest Xbox cost 299 and games cost X dollars each Wayne plans to purchase one Xbox and one game spending a total of 344 wri
    15·2 answers
  • Which statements about triangles ABC and DEF are true?<br> ​<br> ​Select all that apply.
    6·2 answers
  • Help pls. I have been stuck on this for 15 minutes now.​
    12·2 answers
  • Find the area of a rectangle with side lengths 3/5 inch and 5/6 inch
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!