The area of a rectangle is 45 cm2. two squares are constructed such that two adjacent sides of the rectangle are each also the side of one of the squares. the combined area of the two squares is 106 cm². find the lengths of the sides of the squares.

The length of sides of one square is 5cm  and length of sides of another square is 9cm

Step-by-step explanation:

Let the length of rectangle be x and width of rectangle be y.

We have given,

Area of rectangle = 45 cm²

i.e. Area of rectangle = x·y = 45  or xy = 45   ---------(1)

Next, two squares are constructed from two adjacent sides of rectangle.

i.e Side length of one square will be x and side length of another square will be y.

Area of one square = x²

And area of another square = y²

According to problem,

Sum of area of two squares is 106 cm²

∴ x²+y² = 106   ---------------(2)

From equation (1) and (2) , we can find x and y.

xy = 45  or x =  , Plug this in equation (2).

We get,

x² + y² = 106

or

or

or

On solving this equation we get ,

y²=81 or 25

or y = 9 or 5

for y =9 , x=

or for y = 5 , x =

Hence the length of sides of one square is 5cm  and length of sides of another square is 9cm

linear

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