Lisa C.

asked • 09/27/14

Determining height/width of rectangle

I've been given the perimeter and area of squares/rectangles.  I used the quadratic equation to find 2 values: =(P+-(sq.rt((P*P)-16A)))/4 (sorry, my keyboard has no carrot symbol).  Is there any way (other than looking at the rectangle) to determine which value is the height and which is the width?  Thanks.

Yohan C.

Is an area of square & rectangle equal?
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09/27/14

Yohan C.

Is this how you would've written (P+ √P2 - 16A) ?
                                                        4
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09/27/14

Lisa C.

   downloaded a new keyboard, lets see if this works any better.  Thanks 4 the quick responce.  Yes, i have many squares and rectangles that i have a been given both area and perimeter for.  I was wondering if there was a way to determine the height and width of each shape.  I started with the 2 equations for perimeter (P=2x + 2y) and area (A=x*y).  I put thoes in the format ay^2+by+c, obtaining y^2-y(P/2)+A.  From there, i plugged the numbers into the quadriatic formula and got  (P±(P^2-16A)^0.5)/4.  So, i was thinking the 2 numbers i get are the height and width of the rectangles.  However, without actually looking at the rectangle, is there a way i can figure out which us whuch?  Does the + produce height values, - width?  Hope this explains my question a littke better.  TIA.
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09/27/14

Yohan C.

Let's revisit the difference between squares and rectangle.
Both has 4 right angles.  Both has 4 sides.  Both shapes have their opposite side parallel and equal.
 
Difference is square has 4 equal sides and rectangle has 2 equal-opposite-side (2x & 2y).  So, if you get two different positive values, you are good.  That will determine that you have a rectangle.  As you can recall, x and y are and have different values. 
 
 
 
It doesn't matter which one is height or width.  Think like this way: imagine the mattress laying down vs. stand against the wall.
 
All measurements are & must be positive.  There are no negative measurements whatsoever.
 
 
 
Where did you get ay^2+by+c, obtaining y^2-y(P/2)+A and (P±(P^2-16A)^0.5)/4?
 
 
 
If it is negative, it will determine its direction or magnitude.  But not actual measurement.  Just for heads up and future reference (if you are planning to take science class).
 
 
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09/27/14

1 Expert Answer

By:

Arthur D. answered • 09/27/14

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A=lw
P=2l+2w
A/w=l
P=2(A/w)+2w
wP=2A+2w2
2w2+2A-wP=0
if you are given the Area and the Perimeter, substitute them into this equation
example: Area=28 square units and Perimeter=22 units
2w2+2(28)-w(22)=0
2w2+56-22w=0
2w2-22w+56=0
w2-11w+28=0
(w-7)(w-4)=0
w-7=0
w=7 units
w-4=0
w=4 units
A=7*4=28 square units
P=2(7)+2(4)
P=14+8
P=22 units
the length and width of a rectangle are interchangeable; either measurement can be the width and either measurement can be the length
 
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