A blue sqaure is placed inside a large yellow square The centres of the squares are aligned one over the other one side of the square is (3x + 2)cm and the other side is (8 - x)cm the area of the blue square is 36% the area of the yellow square. Find the dstance between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner

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

Step-by-step 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

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)

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