This figure is not drawn to scale. It is made up of 3 squares. The ratio of the area of the smallest square to the largest square is 2:9 while the shaded area is 3/7 of the unshaded area. What is the ratio of the shaded area to the area of the smallest square?
Let A be the total area of the largest square
The smallest square occupies [ (2 ) / (2 +9)]A = 2/11 of the total area = (2/11)A
The shaded area occupies [ (3) / (3 + 7)]A = 3/10 of the total area = (3/10)A
Shaded area (3/10)A (3/10)
____________________ = ______ = ____ = (3/10) (11/2) = 33/20 = 33 : 20
Area of smallest square (2/11)A (2/11)
Let the area of small square he S
Shaded area be x.
Unshaded area be y.
as the largest square is made up of shaded and unshaded area So area of largest square = x + y.
Now given ratio of area of smallest square to largest square is 2:9.
i.e. S/(x + y) = 2/9 - 1
ratio of shaded area & unshaded area is 3:7.
(Shaded area)/(Unshaded area) = 3/7
x/y = 3/7
7x = 3y
y = 7/3x
put value of y in 1
S/(x + 7/3x) = 2/9
9s = 2(x + 7/3x)
9s = 20x/3
27/20 = x/s
27/20 = (Shaded area)/(Smallest Square)
Ratio of shaded area to the area of smallest square is 27:20
I got the same as slimesewer, good work!
Sorry Chris, I believe you made a mistake somewhere.
I draw the scale pic (just for fun)
I actually used a different, although probably not easier method to Slimesewer
I said that if the ratio fo areas is 2 to 9
then the ratio of the sides is sqrt2 to sqrt9
hence on my pic the first sides I could label were sqrt(2) *x and 3x
Then I took it from there.