the length of a rectangle is 8 cm more than its width. If the length is decreased by 9 and the width is tripled, the area is increased by 50%. What was the area of the original rectangle?

Answer 1

x=B,L=x+8, 3/2(x+8)(x)=(x+8-9)(3x),3/2(x(x)+8x)=3x(x-1), 3x(x)+24x=2(3x(x)+3x,factorisex,6x-6=3x+24,x=10,A=18(10),A=180

Answer 2

Are we supposed to decipher what all that is ?

Math is a precise language, and as such needs proper statements and presentation.

Sample:

let the width be x cm
then the length is x+8 cm
original area = x(x+8) cm^2

new width = 3x cm
new length = x+8 - 9 = x-1 cm
new area = 3x(x-1)

new area = 1.5(old area)
3x(x-1) = 1.5(x(x+8))
3x^2 - 3x = 1.5x^2 + 12x
1.5x^2 - 15x = 0
3x^2 - 30x = 0
3x(x - 10) = 0

3x = 0
x = 0 , not very likely

or

x = 10

original rectangle was 10 by 18 for an area of 180
new rectangle was 30 by 9 for an area of 270


Check:
What is 150% of 180? Why , sure enough it is 180