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1. A rhombus has an area of 9cm2. The area is multiplied by 5. Describe the effects on the diagonals of the rhombus.


2. A circle has a circumference of 14pi ft. The area is halved. Describe the effects on the circumference.

 Jun 1, 2016
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1.   The area of a rhombus - in terms of its diagonals - is :

 

[d1* d2] / 2      where d1 and d2 are the diagonal lengths

 

So.......the original area has been quintupled.......the effect on each diagonal is to increase the original length by √5......to see why this is so......let the original area =

 

[d1 * d2]/ 2

 

Now....increase each diagonal lenght by √5   and we have

 

Area =   [√5d1 * √5d2] / 2    =  5 [d1*d2] / 2    =  5 times the original area

 

 

2.  If the area is halved.......the circumference is 1/√2  as much as before

 

To see this.......note that if the original circumference was 14pi  ft....the radius = 7 ft

And the original area = pi*r^2  =  pi*49   = 49pi ft^2

 

So.....1/2 of this =  49pi/2  ft^2.....and we can solve for the new radius thusly :

 

49pi/2 = pi *r^2      divide by pi on both sides

 

r^2  = 49/[2]

 

r = 7/ [√2]  ft

 

So....the new circumference  = 2 * pi * [7/√2]   =  14pi/√2  = 14pi * (1/√2) ft

 

 

 

cool cool cool

 Jun 1, 2016

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