Question

The ratio of the area of square X to the area of square Y is 1:4.
1/5 of square X overlaps with square Y.
(a) find the ratio of the unshaded area of square X to the unshaded area of square Y,

(b) given that the area of square Y is 324 cm2, find the length of square x.

Answer 1

Ratio of area of x : area of y = 1 : 4

Let k be the constant ratio:

Ratio of area of x : area of y = k : 4k

Find the overlapping area:

1/5 of k = 1/5k

Find the ratio of the non-overlapping area:

Ratio of area of x : area of y = k - 1/5k : 4k  - 1/5k

Ratio of area of x : area of y = 4/5 k : 19/5 k

Ratio of area of x : area of y = 4k : 19k

Therefore,  the ratio is 4 : 19

Find the area of x:

Given that area of y = 324 cm²

4k = 324

k = 324 ÷ 4 = 81 cm²

Find the length of square x:

area = length²

length² = 81

length = √81

length = 9 cm

Answer: The ratio is 4 : 19 and the length of x is 9 cm