Mathematics High School

MATHEMATICAL CONNECTIONS Find the dimensions of the polygon with the given area.
Area = 44 ft2

MATHEMATICAL CONNECTIONS Find The Dimensions Of The Polygon With The Given Area.Area = 44 Ft2

Answers

Answer 1

Answer:

Length = 11

Width = 4

Step-by-step explanation:

Answer 2

The value of dimension are;

Length of polygon is 11 ft.

Width of polygon is 4 ft.

Here,

Area of polygon = 44 ft^2

Length of polygon = ( x - 5 ) ft

Width of polygon = ( x - 12 ) ft

We have to find the dimension of polygon.

What is the polygon?

A two-dimensional geometric figure that has a finite number of sides, is called polygon.

Now,

Area of polygon = 44 ft^2

Length of polygon = ( x - 5 ) ft

Width of polygon = ( x - 12 ) ft

Since, Area of polygon = length x width

Hence,

[tex]44 = ( x - 5 ) ( x - 12 )\\\\44 = x^{2} -5x-12x+60\\\\x^{2} - 17x + 16 = 0[/tex]

After factorizing we get;

[tex]x^{2} - 16x - 1x + 16 = 0\\\\x ( x-16) -1 ( x - 16)= 0\\\\(x-1)(x-16)=0[/tex]

[tex]x = 1, x = 16[/tex]

Since, x = 1 is not possible because its gives the values of dimension in negative.

So, x = 16

Now,

Length of polygon = ( x - 5 ) ft = 16 - 5 = 11 ft

Width of polygon = ( x - 12 ) ft = 16 - 12 = 4 ft

Therefore, Length of polygon is 11 ft.

                Width of polygon is 4 ft.

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