The area of a rectangular piece of land is 280 square meters. If the length of the land was 5 meters less and the width was 1 meter more, the shape of the land would be a square.

Part A: Write an equation to find the width (x) of the land. Show the steps of your work. (5 points)

Part B: What is the width of the land in meters? Show the steps of your work. (5 points)

Question

The area of a rectangular piece of land is 280 square meters. If the length of the land was 5 meters less and the width was 1 meter more, the shape of the land would be a square.

Part A: Write an equation to find the width (x) of the land. Show the steps of your work. (5 points)

Part B: What is the width of the land in meters? Show the steps of your work. (5 points)

anonymous · Answer

@Mr.ClayLordMath Help?

anonymous · Answer

@sourwing Help?

whpalmer4 · Answer

what's the area of a rectangle?

whpalmer4 · Answer

Area of a rectangle is $$A = l*w$$where $w$ is the width and $l$ is the length.  We know the area of this rectangle is 280, so $280 = l * w$.  

Next, we know that if we change the length to be 5 meters less, and the width to be 1 meter more, they will be equal (because the shape will be a square).  That implies that
$$l-5 = w+1$$

Using the two equations
$$280 = l * w$$$$l-5=w+1$$you can work out the values of the length and width.

whpalmer4 · Answer

I would suggest an easy approach might be to solve the second equation for $l$, then plug whatever that expression is in place of $l$ in the first equation.  That will give you a formula in terms of $w$ which you can solve.  Note that you'll get two solutions, as it is a quadratic equation, but only one will make sense in this problem.