Question

The area of a rectangular piece of land is 240 square meters. If the length of the land was 5 meters less and the width was 3 meters 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.

Part B: What is the width of the land in meters? Show the steps of your work

Answer 1

@wio can you help? I think I got it wrong

Answer 2

I started with length-5=width+3

Answer 3

@lucaz: you're correct for the first part. Now, you'd need to form an equation which relates the length and width to the area. Can you try to form this equation?

Answer 4

I did it, length=width+8
area=(width+8)(width+3), but what would that equal to?

Answer 5

oh, I think it should be area=(width+8)^2
or area=(length-8)^2

Answer 6

no, you should find the area of the rectangle - what is this equal to (in terms of the length & the width)?

Answer 7

length*width

Answer 8

So can you express the area in terms of only 1 variable (i.e. choose either length or width)?

Answer 9

first I tried area=(width+8)(width+3)

Answer 10

No, shouldn't area = length* width? And the length = width+8? So, what does that make the area?

Answer 11

w(w+8)?

Answer 12

Yes & you know (from the question) that the area = 240m^2. So can you express this in an equation?

Answer 13

w^2+8w=240 right?

Answer 14

Yes, & that's the answer to Part A of the question. Now, can you work out this equation & solve for the width?

Answer 15

I think w=12

Answer 16

You're correct. Well Done!

Answer 17

silly mistake in the beginning, thank you!

Answer 18

You're welcome.