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James had a rectangular piece of art paper. He painted 2/5 of it yellow, 1/3 of it purple and 1/2 of the remaining space pink. He had 240 cm² of the paper left to be painted. If the length of the whole art paper was twice its breadth, what was its perimeter?

 May 7, 2024
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Area =  L * B =     2B * B  = 2B^2

 

Yellow and Purple area =  (2/5 + 1/3) * 2B^2  =  (22/15)B^2

Pink area  = (1/2) ( 2B^2  - 22/15 *B^2 ) =  (4/15)B^2

 

So

 

Area - Painted Area =   240

 

2B^2 - (22/15 + (4/15))B^2  =  240

 

[4/15) B^2 =  240

 

B^2  = (240* 4 /15)  

 

B^2  = 960 / 15

 

B^2  =  64

 

B = 8

 

2B =  16

 

Perimeter  =  2 [ B + 2B ]  =   2 [ 8 + 16 ] =    48 cm

 

 

cool cool cool

 May 7, 2024

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