if a square and a rhombus have all sides 10, would they haev

Question

if a square and a rhombus have all sides 10, would they haev the same area of 100?

Fig · Answer

A square is a special rhombus. That said, most rhombus are not squares. So, the answer is "No, usually and yes, seldom"

walker · Answer

excellent answer

GMAT TIGER · Answer

so in this case, the square and rhombus both have equal sides. so the rhombus is also a square. correct?

GK_Gmat · Answer

Unless the angle measure of the rhombus are 90 degrees, the answer is no.

bmwhype2 · Answer

so...

if we want to  maximize  the area of a figure that has two adjacent sdies of 10, we go with the square rather than the rhombus?

Fig · Answer

Yes... My view on it under... (Out of GMAT) Let: > h be the height of a rombhus > w be the width of a rombhus o (w/2)^2 + (h/2)^2 = 10^2 <=> w^2 + h^2 = (20)^2 => 2*w + d(h^2)/dw = 0..... we derivate by dw <=> 2*w + 2*h*dh/dw = 0 <=> w = -h * dh/dw <=> w/-h = dh/dw Then, the area is such: o Area = (h)*(w)/2 The maximum of area is obtained for an extremum, implying that if we derivate by dw or dh, we obtain 0. dArea/dw = 0 <=> w*dh/dw + h*dw/dw = 0 <=> w*w/-h + h*dw/dw = 0 <=> -w^2 + h^2 = 0 <=> w^2 = h^2 <=> w = h The square is the optimized rombhus to contain the most

bmwhype2 · Answer

fig, you are brutal :shock:

Fig · Answer

It's out of the scope

... yet a way to see it as true

walker · Answer

Wow, Fig! <img src="{SMILIES_PATH}/icon_biggrin.gif" alt=":-D" title="Very Happy" />

Fig · Answer

Some rest of my school

... Who said that derivates serve to nothing :p By the way, u are not that bad too in Q

... When do u plan to pass the GMAT?

walker · Answer

I'm going in February. I still have low verbal (but I'm improving it step by step

)

Fig · Answer

I was in your shoes more than a year ago

... The V section asked me to put a lot of effort and dedication... Good luck to u! (Even if the luck should not be the key to crack the V section we agree...)

walker · Answer

Thanks! <img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" />

Whatever · Answer

My answer is NO unless rhomb is a square:

Square: 10*10 = 100.

Rhomb: Base * height (as rhomb could be a type of parallelogram)
Suppose 2 of the angles are equal 45 (or 60 - does not matter) Then the height is equal to 5*sqrt(2) and the square = 10 * 5*sqrt(2) = 50 * sqrt(2)

if a square and a rhombus have all sides 10, would they haev

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