A poultry farmer fenced a regular plot of land in rectangular shape.the length of the plot is 3metres more…

Question

A poultry farmer fenced a regular plot of land in rectangular shape.the length of the plot is 3metres more than it's width given that the total area of the plot is 180centimetres squared A,form a quadratic equation to represent this situation

ScanSolve AI Tutor · Accepted Answer

There is a unit inconsistency in the problem statement: the length difference is given in metres, while the area is given in centimetres squared. For a "plot of land" for a "poultry farmer", it is highly probable that the area should be in square metres to be consistent with the length difference in metres and to represent a realistic plot size. I will proceed with the assumption that the area is $\text{180 metres squared}$ .

Define variables.
Let $w$ be the width of the rectangular plot in metres.
Let $l$ be the length of the rectangular plot in metres.
Formulate equations based on the given information.
The length of the plot is 3 metres more than its width:
$l = w + 3$
The total area of the plot is 180 square metres (based on the assumption):
$\text{Area} = l \times w = 180$
Substitute the expression for $l$ into the area equation.
Substitute $l = w + 3$ into the area equation:
$(w + 3)w = 180$
Expand and rearrange the equation into the standard quadratic form $ax^2 + bx + c = 0$ .
$w^2 + 3w = 180$
Subtract 180 from both sides to set the equation to zero:
$w^2 + 3w - 180 = 0$

A poultry farmer fenced a regular plot of land in rectangular shape.the length of the plot is 3metres more than it's width given that the total area of the plot is 180centimetres squared A,form a quadratic equation to represent this situation

Answer

Step-by-step solution

Define variables.

Formulate equations based on the given information.

Substitute the expression for $l$ into the area equation.

Expand and rearrange the equation into the standard quadratic form $ax^2 + bx + c = 0$ .

Try one yourself

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More English Questions

A poultry farmer fenced a regular plot of land in rectangular shape.the length of the plot is 3metres more than it's width given that the total area of the plot is 180centimetres squared A,form a quadratic equation to represent this situation

Answer

Step-by-step solution

Define variables.

Formulate equations based on the given information.

Substitute the expression for lll into the area equation.

Expand and rearrange the equation into the standard quadratic form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0.

Try one yourself

Still stuck on this one?

More English Questions

Substitute the expression for $l$ into the area equation.

Expand and rearrange the equation into the standard quadratic form $ax^2 + bx + c = 0$ .