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kadeem has 58m of fencing to build a four-sided fence around a rectangular plot of land. the area of the land is 204 square meters. solve the dimensions of the field. (length and width)

Sagot :

I’m not quite sure what you mean so do this equation



64837//294738383&38373736

The dimensions of the rectangular plot of the land is 17 × 12 square units.

What is perimeter?

The perimeter of a shape is the distance around the shape. It is the total length of the shape's sides.

What is the formula for the perimeter of rectangle?

Perimeter of rectangle = 2( length + width)

What is area?

The area can be defined as the space occupied by a flat shape or the surface of an object.

What is formula for the area of rectangle?

Area of rectangle = length × width

According to the given question.

Let the length and width of the rectangular plot be x and y respectively.

Kadeem has 58m of fencing.

⇒ Perimeter of the rectangular plot of land = 58m

⇒ 2(length + width) = 58

⇒ x + y = 29...(i)

Also, area of plot land = 204 square units.

⇒ x × y = 204

⇒ x × (29 - x) = 204

⇒ [tex]29x -x^{2} = 204[/tex]

⇒ [tex]x^{2} -29x + 204=0[/tex]

⇒ [tex]x^{2} -12x -17x +204=0[/tex]

⇒ [tex]x(x-12)-17(x -12)=0[/tex]

⇒ [tex](x -12)(x -17) = 0[/tex]

⇒ x = 12 or x = 17

When, [tex]x = 12[/tex]

[tex]y = 29-12 = 17m[/tex]

And when, [tex]x = 17[/tex]

[tex]y = 29 - 17 = 12m[/tex]

Hence, the dimensions of the rectangular plot of the land is 17 × 12 square units.

Find out more information about perimeter and area of rectangle here:

https://brainly.com/question/16572231

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