Question

A pool company is creating an image for a client that has the look of a 3-D image for a family pool and a similar dog pool. Find the value of c in the drawing below:

Quadrilaterals LMNO and PQRS are shown. Side LM measures 4, side MN measures 6, side NO measures a, side OL measures 7, side PQ measures 2, side QR measures c, side RS measures 5, side SP measures b.

Numerical Answers Expected!

Answer for Blank 1:

Answer 1

An architect planned to construct two similar stone pyramid structures in a park. The figure below shows the front view of the pyramids in her plan, but there is an error in the dimensions:

Two similar scalene triangles PQR and ABC with angle P congruent to angle A, angle Q congruent to angle B, and QR and BC as the bases of the triangles. The length of PQ is 9 feet, the length of QR is 10.5 feet, and the length of RP is 7.5 feet. The length of AB is 6 feet, the length of BC is 7 feet, and the length of CA is 4.5 feet.

Which of the following changes should she make to the length of side CA to correct her error?

Change the length of side CA to 6 feet
Change the length of side CA to 3 feet
Change the length of side CA to 5 feet
Change the length of side CA to 8 feet

Answer 2

those are it

Answer 3

ok the thing about similar shapes, is that the sides are proportional to each other

Answer 4

as long as you are comparing a side to the corresponding side

Answer 5

ok

Answer 6

so side LM is proprotional to side PQ

Answer 7

and side O N is proportional so sides SR

Answer 8

ON*

Answer 9

we want to find c which is the side QR, which side is proportional to it?

Answer 10

6 on side MN

Answer 11

ok, i cant really think of the steps leading up to this, but the proportion of ML- QP must be equal to the proportion MN-QR

Answer 12

if you've ever learned ratios or remember it,
we can write the propertion ML-QP as
\[\frac{4}{2}\]

Answer 13

and that is equal to the proportion MN-QR
so \[\frac{4}{2}= \frac{6}{c}\]

Answer 14

and the other as 6 over c?

Answer 15

and then you can solve for c, but it should be really obvious by looking at it

Answer 16

yeah u just did it lol

Answer 17

c=?

Answer 18

im not so sure yikes..

Answer 19

2

Answer 20

or 4

Answer 21

4/2 is 2, yes
so 6 divided by what is equal to 2?

Answer 22

3

Answer 23

here let me changes the proportion around if it helps
\[\frac{2}{4}=\frac{c}{6}\]

Answer 24

thats the same thing, and yes c = 3

Answer 25

any questions about it?

Answer 26

oh great so the answer is 3? and no i got it thanks so much (:

Answer 27

ok, moving onnnn

Answer 28

the problem states, we have 2 similar triangles

Answer 29

yupp last one yay lmao

Answer 30

if you remember what similar triangles mean, the triangles share the same corresponding angles,
so angle B=Q R=C, etc

Answer 31

yes

Answer 32

now, the problem states, there is a problem with side length CA

Answer 33

so we completely ignore the 4.5ft, and assume its a side length of "x"

Answer 34

ok

Answer 35

now, remember what we did with the last problem,

for similar shapes, that means the corresponding sides are proportional to each other

Answer 36

so what side is CA proportional to?

Answer 37

riight like we just did with the division

Answer 38

RQ

Answer 39

wrong

Answer 40

nooo

Answer 41

mistake sorry

Answer 42

i mean RP

Answer 43

RP

Answer 44

yes

Answer 45

so 4.5 ft is proportional to 7.5 ft

Answer 46

ok, if we want to put it interms of a fraction its
\[\frac{x}{7.5}\]

Answer 47

no, remember the problem said 4.5 is wrong

Answer 48

oh right i forgot its X

Answer 49

ok, now we want to look at a known proportion,

it might be BC-QR or AB-PQ

Answer 50

pick one of them

Answer 51

bc qr

Answer 52

so the ratio between the two are?

Answer 53

10.5 and 7.0

Answer 54

7.0 and 10.5, respectively since we wrote it as BC- QR

Answer 55

now if we compare the 2 ratios to each other, it might look something like
\[\frac{x}{7.5}=\frac{7}{10.5}\]

Answer 56

and now we solve for x which is side length CA

Answer 57

and the answer isssss?

Answer 58

its ok to grab a calculator for this

Answer 59

but, for equations, what you want to do is multiple 7.5 to both sides

Answer 60

ya i need a calculator for this i lost mine so i have to find one on google

Answer 61

should i look for like a geometry calculator?

Answer 62

dosent matter, a basic calculator will work

Answer 63

ok

Answer 64

\[7.5*\frac{x}{7.5}=7.5*\frac{7}{10.5}\]
\[x=7.5*\frac{7}{10.5}\]

Answer 65

your computer should have a calculator

Answer 66

but u can't write x on it

Answer 67

we're solving for x
you dont need to write x

Answer 68

you just need to calculate the other side

Answer 69

its 5

Answer 70

we isolate x on one side by multiplying 7.5 to both sides

the 7.5 on the left side cancels out

Answer 71

yes

Answer 72

omg i was like thinking 5 even before e started the problem lmao

Answer 73

like for the answer

Answer 74

guessing doesnt help

Answer 75

well, only educated guesses, but i highly doubt it was

Answer 76

any questions?

Answer 77

but it was still right. and it was. i wasn't completely just guessing. i was thinking 5 because 4.5 is closest to 5

Answer 78

and every other number on that side was closest to hundreths place

Answer 79

ok, it was a slight educated guess

Answer 80

by looking at the magnitutde of the numbers

Answer 81

well i guess lol

Answer 82

good job

Answer 83

thanks for ur help

Answer 84

good night

Answer 85

now you should get a 100 on your next quiz, right?

Answer 86

thats what I'm hoping for

Answer 87

good, night then

Answer 88

now gotta get some zzzzz

Answer 89

night