A simple rectangle... *(Re-posted with changed options)*

Geometry Level 3

If the base of the rectangle is increased by 10 % and the area is unchanged, then the altitude is increased by ?


Wanna try more simple problems

11 1 9 -11\cfrac { 1 }{ 9 } % 9 1 11 -9\cfrac { 1 }{ 11 } % 11 1 9 11\cfrac { 1 }{ 9 } % 9 1 11 9\cfrac { 1 }{ 11 } % none of these

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1 solution

Soumo Mukherjee
Jan 17, 2015

The increased base is b + b × 10 100 = 11 10 b b+b\times \cfrac { 10 }{ 100 } =\cfrac { 11 }{ 10 } b . Similarly the increased altitude must be of the form ( x h ) \left( xh \right) , where h h is the initial values of the altitude.

According to the problem we have ( 11 10 b ) ( x h ) = b h \left( \cfrac { 11 }{ 10 } b \right) \left( xh \right) =bh . Solving it for x x , we get x = 10 11 x=\cfrac { 10 }{ 11 } . Therefore the final altitude after the transformations is 10 11 h \cfrac { 10 }{ 11 } h . Increase in altitude is ( f i n a l a l t i t u d e ) ( i n t i t i a l a l t i t u d e ) ( i n t i t i a l a l t i t u d e ) × 100 \cfrac { \left( final\quad altitude \right) -\left( intitial\quad altitude \right) }{ \left( intitial\quad altitude \right) } \times 100 or ( 10 11 h ) h h × 100 = 9 1 11 \cfrac { \left( \cfrac { 10 }{ 11 } h \right) -h }{ h } \times 100=\boxed { -9\cfrac { 1 }{ 11 } } %. Hence the answer.

Note that if you ever need to change the answers to a question, you can just tag @Calvin Lin and he will do it for you, making sure that everyone who should have gotten credit did get credit.

Moderators can do it too, but I'm not sure if we're allowed to do it yet.

Daniel Liu - 6 years, 4 months ago

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The best approach would be to report the problem and state that you want to update the answer, which would leave a record and also notify others who are wanting to report it. @mentions might not work if I'm flooded with them.

Calvin Lin Staff - 6 years, 4 months ago

Thanks...

and

I am about to post a problem now \stackrel{\wedge\,\wedge}{\smile} .

Soumo Mukherjee - 6 years, 4 months ago

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