Solve this if u can......!!,!

Geometry Level 3

Area of a triangular surface is calculated as 1/2 X altitude X base. If altitude of a triangle is increased by 5% and the base of the same triangle is increased by 7%. What percent would the area of the triangle increase?


The answer is 12.35.

Ayushman Chahar by Ayushman Chahar , 21, India

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2 solutions

Sunil Pradhan
Dec 11, 2014

Two successive increase by a% and b% then overall increase

% increase = a + b + ab/100

= 5 + 7 + 35/100 = 12.35%

1 Helpful 0 Interesting 0 Brilliant 0 Confused

sir ........ isnt that the formula for overall increase wen 2 quantities (related to the overall quantity) are simultaneously increased??

Ganesh Ayyappan - 6 years, 5 months ago
Ritu Roy
Nov 15, 2014

L e t t h e o r i g i n a l △ h a v e t h e a r e a a s A = 1 2 b h A r e a o f n e w △ A ′ = 1 2 ( 107 100 b . 105 100 h ) Let\quad the\quad original\quad \triangle \quad have\quad the\quad area\quad as\\ A\quad =\quad \frac { 1 }{ 2 } bh\\ Area\quad of\quad new\quad \triangle \\ A'\quad =\quad \frac { 1 }{ 2 } (\frac { 107 }{ 100 } b.\frac { 105 }{ 100 } h) P e r c e n t a g e o f i n c r e a s e i n a r e a o f n e w △ = A ′ − A A . 100 = [ ( 1 2 . 107 100 b . 105 100 h ) − ( 1 2 b h ) ] 1 2 b h . 100 = 1 2 b h ( 107.105 100.100 − 1 ) 1 2 b h . 100 = ( 11235 100 − 100 ) = 12.35 Percentage\quad of\quad increase\quad in\quad area\quad of\quad new\quad \triangle \\ \quad \quad =\quad \frac { A'-A }{ A } .100\quad \\ \quad \quad =\quad \frac { \left[ \left( \frac { 1 }{ 2 } .\frac { 107 }{ 100 } b.\frac { 105 }{ 100 } h \right) -\left( \frac { 1 }{ 2 } bh \right) \right] }{ \frac { 1 }{ 2 } bh } .100\\ \quad \quad =\quad \frac { \frac { 1 }{ 2 } bh\left( \frac { 107.105 }{ 100.100 } -1 \right) }{ \frac { 1 }{ 2 } bh } .100\\ \quad \quad =\quad \left( \frac { 11235 }{ 100 } -100 \right) \\ \quad \quad = \quad \boxed {12.35}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Correct.....

Ayushman Chahar - 6 years, 7 months ago

i did the same

Ganesh Ayyappan - 6 years, 5 months ago

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