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Find the base of the new rectangle

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RASTA

RASTA aktiv_icon

19:06 Uhr, 21.11.2022

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Tag!
I need your help to see if this problem is correct and if not what I did wrong.
thanks in advance,

''The perimeter of a rectangle is 44m. If the base of this rectangle were 3 meters longer and its height 4 meters less, the area of the new rectangle would be 30 square meters less than the area of the first rectangle. Find the base of the new rectangle''.

I kind of lean in this direction
data given
P=2(b)+2(h)
Perimeter=44 m
so if P=44, then,
bh=22

2(a)+2(b)=44

a+b=22

3a+3b=66

If the base of this rectangle were 3 meters longer =(b+3)
and its height 4 meters less =(h-4)
then,
the area of the new rectangle would be 30 square meters less than the area of the first rectangle.
then I set it up like this,


(b×h)−(b+3(h−4) =30m2

bh−(bh−4b+3h−12) =30m2

bh−bh+4b−3h+12=30m^2

4b−3h+12=30m^2

4b−3h=30〖−12〗
4b−3h=18

I went back to re-take my first equation and add my last one to it

3h+3b=66
−3h+4b=18

7b=84

b=12

the new base of the new triangle is 12m

is this okay?

Vielen Dank.




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walbus

walbus aktiv_icon

19:28 Uhr, 21.11.2022

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2(a+b)=44
a+b=22
a=22-b

A=ab=(22-b)b

(22-b+3)(b-4)=(22-b)b-30

b=...

a=...







RASTA

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21:12 Uhr, 21.11.2022

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I am sorry walbus, there is a typo in my first post which may change things
i wrote hb=22 when it should have been h+b=22

dose that change your setup, or not?
because I simplified your setup and got b=10, but that is not good,
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Roman-22

Roman-22

22:17 Uhr, 21.11.2022

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You got confused with b,h vs. a,b! You yourself used both different set of names which sure is something to avoid!

It once again shows that it does not make much sense to use one-letter-names without explaining what is meant.

You got base length b=12m which is the correct answer.

In walbus' answer b is the heigth and a is the base. So his b=10 is correct, too. because of a=22-b=12 he gets the same result as yours.

Actually I don't understand his answer. You asked "is this okay?" and the answer should simply have been "Yes!".
Of course apart from the typo you mentioned yourself and the confusing mix (b;h) vs. (a;b).
And even though the question definitely was "Find the base of the new rectangle", his approach would in first case get you the height which he has chosen to name "b".
RASTA

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01:04 Uhr, 22.11.2022

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Yes, ROmans. you're right. I should have stuck to b for base and h for height.
Walbus b for height threw me off completely. Honestly, don't know why he chose b because in German height is Höhe , right?. So, the logical variable of choice would have been h.
But I am thankful to him for his answer and interest. Thanks to you to my friend!
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Roman-22

Roman-22

03:40 Uhr, 22.11.2022

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Its sure not unusual to name the sides of a rectangle a and b. And if you draw a rectangle it would be quite natural to name the horizontal length a and vertical b as walbus had done.

But as your text is talking about a "base" and a "height", it would have been necessary to clearly state which variable name is supposed to indicate the "base" and which the "height" (and yes, in this case using b and h as names is the better choice).
This is a recurring problem, even here in the forum, that answers (usually well-intentioned) are given that are often relatively meaningless because there is no explanation of what the variables and terms presented are supposed to represent.

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