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?

Guest Mar 28, 2022

edited by
Guest
Mar 28, 2022

#1**+2 **

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)

CPhill Apr 1, 2022

#2**+2 **

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

Slimesewer Apr 3, 2022

#3**+1 **

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)

Melody Apr 3, 2022