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/sci/ - Science & Math

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3874748 No.3874748 [Reply] [Original]

Crudely drawn, but I hope you get the point.
Here's what I tried doing:

A = (D + d)/ 2
<=> 5 = (d + 3)d/2
<=> 10 = d + 3d
<=> 10 = 4d
<=> d = 10/4
<=> D = 5,5 ∧ d = 2,5

But the answers page says d = 2 ∧ d = 5.
The info in my image is correct. Is the book wrong or did I miss something?

>> No.3874771

>A = (D + d)/ 2

check dimensions

>> No.3874779
File: 160 KB, 466x500, 1300643534344.jpg [View same] [iqdb] [saucenao] [google]
3874779

>>3874771
Woops, I messed up there, but I did do
>5 = (d+3)d/2
which is right. Am I right?

>> No.3874782

A=4*D*(D-3)/2
solve for D

>> No.3874793

>>3874782
Why 4*D? Because of the sides?

>> No.3874801

http://www.wolframalpha.com/input/?i=%28d%28d%2B3%29%29%2F2+%3D+1.25

Possibly?

>> No.3874828

>>3874801

Disregard this, I assumed that the d and D represented the lengths of each quadrant, not the entire shape. In that case refer to this, it's the bare bones behind the question including the correct answer.

http://www.wolframalpha.com/input/?i=%28d%28d%2B3%29%29%2F2+%3D+5

>> No.3874830

>>3874801
I had tried that and several others but neither of them gave me d = 2.

Also, >>3874782
I tried doing it with the 4*D and it gave me 10/4. Look:
10 = 4D^2 - 12D
10 = 4D
D = 10/4
which gives d a negative value, which can't be. I think you're wrong.

>> No.3874842

Look at as two rectangles of size d*D.

Hence A =2(d*D)

You'll get a quadractic, solve, PROFIT!

>> No.3874851

>>3874830

>>3874782

Assumed the same as I. That the letters represented dimensions of each quadrant not the entire shape, hence the reason for multiplying the result by 4.

>> No.3874877

>>3874842
What do you mean two rectangles? One divided by the red line, or the big blue rectangle divided by D?

>> No.3874880
File: 4 KB, 310x174, ungh.png [View same] [iqdb] [saucenao] [google]
3874880

>>3874877

>> No.3874892

5= 1/2(d+3)(d)
5=(d^2+3d)/2
10=d^2+3d
0=d^2+3d-10
~(d+5)(d-2)
d=-5 or d=2
d>0, so d=2
D=5, d=2

>> No.3875043
File: 9 KB, 577x577, rhombus.png [View same] [iqdb] [saucenao] [google]
3875043

Two triangles, area of one triangle is (d/2)*(D/2), so A=2*D*d/4=D*d/2 (=area of a rhombus).
Since d=D-3 you get A=D*(D-3)/2 and then D^2-3D-2A=0, D=(3/2)±sqrt((9/4)+10)
so D=(5,-2)cm and d=(2,-5)cm