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anonymous
 one year ago
Geometry Help! Please!
anonymous
 one year ago
Geometry Help! Please!

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welshfella
 one year ago
Best ResponseYou've already chosen the best response.1The 4 triangles right angled formed are congruent Let the smallest side of these = x and let the area of shaded part equal y area of each triangle = 2* x/2 = x consider one of the large rectangles y + 2x = 6 consider the shaded part which is a paralelogram the area = base * perpendicular height

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1area= BE * DE  x y = 2* (3  x) y = 6  2x

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1which is the same equation as we had before! how embarrassing!! I must be missing something here.....

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1the area is a rhombus  so is there a formula for this in terms of the sides  or diagonals?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, here is an outline of solution step1 : show that all the four triangles outside the shaded region are congruent dw:1440259209437:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2step2 : By CPCTC, it follows that BG = BH = DH = DG, making BGDH a rhombus

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440259500328:dw

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2solve for x x^2 + 4 = (3x)^2

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2step3 : \(\triangle OBG\sim\triangle ADB \) by \(AA\) similarity, so \(\dfrac{OG}{OB}=\dfrac{2}{3}\) dw:1440259468027:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you can find OB trivially using the fact that OB = BD/2 (diagonals bisect each other in rhombus)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1and the area of the rhombus = pq/2 where p and q are the diagonals right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yes, otherwise it is easy to see that all the four internal triangles are congruent : dw:1440260040970:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\(A_1 = A_2 = A_3 = A_4\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Is it not that it is 6 2x And xis calculated by pythagorean, x=5÷6

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Or I missed something?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you might be correct, but i like similar triangles more :)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1amistre's method is correct also simple really

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Of course we need prove the 2 triangle are equal first

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2why do you want to solve a quadratic when you can setup a simple proportion ?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2lol, its not a quadratic, its linear

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Picking up from @amistre64 \[2^2 + x^2 = (3x)^2\]\[x^2 + 4 = x^26x +9\]\[6x = 94\]\[x = \frac{ 5 }{ 6 }\]The figure is also a parallelogram with height 2 and length 35/6 = 13/6.\[A = bh = (3\frac{5}{6})2 = \frac{13}{3}\]

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1once you know the area of the triangles thats it Yes the congruency proff is necessary

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2it looked like a quadratic to me haha

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1yea  but the x^2 cancel out

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2i mean my brain felt it is a quadratic, so rejected initially ;p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you all are so helpful thanks so much!

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2one thing i aint, is a geometrer ;)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2looking at it again, i find it is simpler and kinda cute !

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1interesting question...
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