geometry question (my daughters math work)?

Question

If the sides of a square are decreased by 3cm, the area decreased by 81cm^2. What were the dimensions of the original square? Type a statement that defines what the variable represents.

Answer 1

ok¡¡

so we have that x = one side of the square (remember, in squares all sides are the same value)
so we can say that the decrasing of the sides by 3cm would be like this: (x - 3)
and that the area decreased by 81 would be like this:
x^2 - 81

Then the statement would be like this:

(x - 3)^2 = x^2 - 81
x^2 - 6x + 9 = x^2 - 81
x^2 - x^2 -6x = - 81- 9
-6x = -90
x = 15

The dimension of the sides of the original square are (x-3) = 15 -3 = 12

it is correct trust me....
Greetings... hope have helped you.¡¡¡¡¡ ☺☻☺☻☺☻☺☻

Answer 2

Let her flunk. I know it'll ruin this semester in geometry but by next semester she'll understand how it was so important to accept help when she needs it. Or take away her tv, computer, internet, days out w/ friends or whatever... do it yourself or have her biological parents do it... whoever she is more obedient to, kinda like a pre-punishment for failing and also as a way to get her more focused on her school work even if for just a while to get her to get a passing grade... "if you refuse to accept help and/OR work harder [which might involve accepting a tutor] to get a better grade, then i shall also refuse to provide you with this unnecessary commodities that you've taken for granted; that is until we reach a compromise where you raise your grades either by studying harder/longer and/or getting some help" also, maybe she'll accept help from friends? a friend that is doing better in class than her? maybe you can pay the friend for tutoring your step-daughter... or how about a study group? encourage her to form a study group or to bring other classmates to your house and you lead the study group, that way you know they're studying/learning their material but it won't be so boring/tedious for everyone and it won't seem like you're lecturing to her...

Answer 3

Let the side of a square be s
then area = s * s = s²
if sides are decreased by 3 cm new sides are (s - 3)
area of new square = (s-3)(s-3) = s² - 6s + 9 cm²
area is decreased by 81 cm²
new area = s² - 81 cm²

so s² - 6s + 9 = s² - 81
s² - s² - 6s = -81 - 9
-6s = -90
s = 15 cm
The new side is 15 cm
original side = 15 - 3 = 12 cm

Hope that helps
~~~

Answer 4

Method 1
√81 + 3
= 9 + 3
= 12 cm

Method 2
(y - 3)^2 = 81
y - 3 = √81
y - 3 = 9
y = 9 + 3
y = 12

Answer 5

A= "Area" == s(squared)

The original area was (s+3) cm squared, equal to (A+81) cm squared"

At s, the area is now (A)

That's not geometry, that's algebra -- two simultaneous equations.

s^2 == A

(s+3)^2 == (A+81),

or,

s^2+6s+9 == (A+81)

Solve for s, and you are there.

Answer 6

let x repesent the side of the square in cm
thn the area is x^2
if the side is decreased by 3 cm, thne the side is now (x-3) cm
so the new area is (x-3)^2
this = 81 given
so, (x-3)^2=81
taking square root
x-3=9
x=12
so original square's side was 12 cm

Answer 7

3 cm + 81 cm = 84 cm

a square is 4 sides equal always

Answer 8

you should let your daughter to do her own homework instead of doing it for her. That way she will learn. Teachers do not need to give children homework if the only purpose was to have the excercise done because they can do it themselves. The purpose of homework is for the child to learn and for the concepts learned in class to be absorbed and practiced. If she is stuck, give her a hint.

Answer 9

let initial side be=a
initial area= a*a=a^2

after decreasing
side=a-3
area=(a-3)*(a-3)=a^2+9-6a

change in area=a^2-{a^2+9-6a}=81
6a-9=90
6a=90
a=90/6=15

Answer 10

x²=A
(x-3)²=A-81
(x-3)²=x²-81
x²-6x+9=x²-81
-6x=-90
x=15 cm