A norman window has the shape of a square with a semicircle mounted on it. Find the width of the window if the total area of the square and the semicircle is to be 190 ft squared?

11.68ft or 11.68 feet

Step-by-step explanation:

From the above question, we are told that:

Area of the square and the Area semicircle is to be 190 ft squared.

We are also told in the question that:

The window has the shape of a square with a semicircle mounted on it.

Hence, the Diameter of the semicircle = Width of the Square

Let the Width of the square = x

Area of a square = Width²

= x²

Let the Diameter of the semi circle = x

Radius of the semi circle = Diameter of the semi circle/2 = x/2

Area of a semicircle = πr²/2

Area of a the semi Circle = π ×(x/2)² /2

= (πx²/4)/2

= πx²/8

Therefore,

Area of a square + Area of a semicircle = 190ft²

= x² + πx²/8 = 190

Cross Multiply

x² + πx² = 190

= x² ( 1 + π/8) = 190

x² = (190)/(1 + π/8)

x² = 136.42573798

x = √136.42573798

x = 11.680142892ft

Approximately x ≈ 11.68ft

Therefore, the width of the window = 11.68ft

5050

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