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?

sugabreaddoughman May 7, 2024

#1**+1 **

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

CPhill May 7, 2024