Question

I've been stuck on this question for an hour now. Can you please help me do it and understand it?

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)

Answer 1

So far I have:

\[A = L*W\]

and that'll be

\[280 = (l -5) (w + 1)\].

Answer 2

so in part A

280 = l*w

so

l= 280/w

then using the new dimensions you have posted and making a substitution

l - 5 = w + 1 since the sides of the square are equal

make the substitution

\[\frac{280}{w} - 5 = w + 1\]

multiply every term by w

\[280 - 5w = w^2 + w\]

or

\[w^2 + 6w - 280 = 0\]

just solve the quadratic for w.

you will have 2 answers, just use the positive... as a measurement can't be negative

hope it helps

Answer 3

the quadratic equation can be factored.

Answer 4

or use the general quadratic formula to get the solutions

Answer 5

Thank you! I found that the width is 14. Am I correct?

Answer 6

that's correct...

Answer 7

Thank you again! :)