Question

Write an algebraic rule for the area of the green region in terms of the length of one panel.

Answer 1

@triciaal

Answer 2

u know area formula right?

Answer 3

To find the area of a rectangle, multiply the length by the width

Answer 4

ya correct!

Answer 5

here what is the total lenght?

Answer 6

The family of Fitzgerald Garcia has decided to have a statue of him placed in the garden. The base of the statue will be 2 feet by 3 feet. A raised rectangular bed will be placed around the statue as shown in the diagram. It will be planted with azaleas. The planting space is the green region in the diagram and must be 50 square feet. You have decided to make a rectangular raised bed using 2 panel lengths on one side and 3 panel lengths on the other side.

That's what the question says....

Answer 7

u wanted the area of the green region right? where do u need help exactly..?

Answer 8

Yes sorry i can be confusing but finding areas can be really tricky for me.
and yes to the green region...

Answer 9

ok then what is the total length of the whole rectangle given in the pic?

Answer 10

2x right? @rachel_0212 ??

Answer 11

yes.

Answer 12

Now what is the lenght of the cement portion?

Answer 13

5

Answer 14

So what is the length of the green region alone?

Answer 15

Hint subtact

Answer 16

so i would subtract 5-2x

Answer 17

no..u must subtact the bigger portion-smaller portion

Answer 18

u understand y..right?

Answer 19

2x-5= -10 ??? right?

Answer 20

why=-10??

Answer 21

because i plugged it in ? i might of done it wrong

Answer 22

no..Now just think about the lenght and width of the green region...u found the lenght which is 2x-5 now can u find the width by following the same steps?

Answer 23

x-5??

Answer 24

very good!! now just multiply length and width to get the area..

Answer 25

x-5 * 2x-5 = 2x^2-25 ????

Answer 26

\[(x-5) * (2x-5)\]
=\[x(2x-5) -5(2x-5)\]

Answer 27

u made a mistake in the multiplication..now what do u get?

Answer 28

its \[2x^2-5x-10x+25\]

Answer 29

Now equate this with area they have given u to find x...

Answer 30

2x ² - 15x + 25

Answer 31

??

Answer 32

yes have they given an area for the green region?

Answer 33

I have another question was that answer for question (A)

Answer 34

we have found the expression for the area of the green region it doesn't end there we must find x right?

Answer 35

oh sorry..u were talking abt the first q in pic..?

Answer 36

@rachel_0212 ??

Answer 37

wait what question where you dong?

Answer 38

i was just helping u find the area of the green region...thats what u asked right?

Answer 39

yes, sorry i was under the impression we were doing question (A)

Answer 40

its the answer for the first q (A) but what we have got is a binomial not a trinomial...

Answer 41

Lets finish it ? :)

Answer 42

it can't be a trinomial unless its 3D..but area is only 2D so its a binomial..

Answer 43

did u understand why its a binomial?

Answer 44

so the answer is bionomial ?

Answer 45

binomial ?

Answer 46

No! rachel the answer is the eq we got before.. did u read the first q ? it has a word trinomial in it right?

Answer 47

But i think that word should be binomial ...

Answer 48

since x has max. power 2

Answer 49

Now did u get it rachel?

Answer 50

so i already got the answer? correct
?

Answer 51

yes

Answer 52

coming to the next q

Answer 53

whats ur idea?

Answer 54

lord Jesus i confused myself so the answer for question(A) is 2x^2-15x+25

Answer 55

ya!!

Answer 56

Now do u have any idea for the 2nd Q?

Answer 57

HINT:it involves the answer to the first question!

Answer 58

mmm no i dont?

Answer 59

well all u need to do is equate the expression u got to 900...coz it will be an equation to find x which is the width

Answer 60

got it?

Answer 61

so my full equation would be?

Answer 62

yes..u tell me..

Answer 63

ok let me write it...
\[2x^2-15x+25=900\]

Answer 64

hope u understood