Answer:
the distance y between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner is 1.3cm
Explanation:
From the information given;
A blue square is placed inside a large yellow square and the centres of the squares are aligned one over the other
So ; if one side of the square is (3x + 2)cm (i.e the blue side)
the other side is (8 - x)cm (i.e the yellow sides)
since the two shapes given are squares ; we can say that:
(3x+2)= (8 - x)
3x +x = 8 -2
4x = 6
x = 6/4
x = 1.5
Let replace x = 1.5 for the sides of the square and find the actual length of the square sides.
So, for the yellow side; we have:
= (8 - x)cm
= (8 - 1.5 ) cm
= 6.5 cm
We all know that the area of the square = l²
then the area of the yellow side = (6.5 cm )²
the area of the yellow side = 42.25 cm²
Let y be the distance between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner
Since the blue region is inside the yellow region; to calculate for the side of the blue region ; we have:
(6.5y -y+y) cm
(6.5 - 2y )cm
The area of the blue side =( (6.5 - 2y )cm)²
The area of the blue side = (6.5 - 2y )² cm²
However; we are also given that :
the area of the blue square is 36% the area of the yellow square.
Thus;
(6.5 - 2y )² = 36/100 × 42.25
(6.5 - 2y )² = 0.36 × 42.25
(6.5 - 2y )² = 15.21
(6.5 - 2y ) =
(6.5 - 2y ) = 3.9
6.5 - 2y = 3.9
6.5 - 3.9 = 2y
2.6 = 2y
y = 2.6/2
y = 1.3 cm
Therefore , the distance y between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner is 1.3cm