Question

The length of a rectangular photograph is 1 cm. less than twice the width. If the area of the photograph is 45cm^2, find the dimensions of the rectangle.

Answer 1

What is the equation to find the area of a rectangle?

Answer 2

l
x w

Answer 3

A = L * W. (Please reserve " x " as the representation of an algebraic quantity.) Use " * " to indicate multiplication.

OK. A = L * W.

How would you express the width of this photograph?


How would you express the length of this photograph?

Answer 4

length is 1 cm

Answer 5

that is less than twice the width

Answer 6

No, it's more complicated than that.

We don't know the width, so we represent the width by W.

"The length of a rectangular photograph is 1 cm. less than twice the width."

Using the variable W, express the length of the photo algebraically.

Answer 7

I'm having trouble expressing this

Answer 8

If the width of the photo is W, how would you express "twice the width?"

Answer 9

2w

Answer 10

Good.

"The length of a rectangular photograph is 1 cm. less than twice the width."

Using your 2W, how would you express the length, L, of the photo, algebraically?

Answer 11

1 cm

Answer 12

so 1 cm times ??

Answer 13

"The length of a rectangular photograph is 1 cm. less than twice the width."

You must start with "2W" and then do something to it. What?

What does "less than" mean?

Answer 14

subtract

Answer 15

2w - 1

Answer 16

no sorry

Answer 17

2x * 1

Answer 18

That 2W - 1 is correct, actually; 2x*1 is far off.

"The length of a rectangular photograph is 1 cm. less than twice the width." This says: take twice the width and then subtract 1 cm from that.

Symbolically, 2W - 1 = L.

Answer 19

oh no

Answer 20

2w-1 * 1

Answer 21

that what i meant

Answer 22

the correct way to represent L is L=2W-1. No more than that.

In summary:

Length of rectangle: L = 2W - 1
Width of rectangle: W

General formula for area of a rectangle: A = L * W.

What is the area of THIS particular rectangle, expressed algebraically / symbolicallyi?

Answer 23

2w^2 - w

Answer 24

w(2w-1)

Answer 25

Good. You are told that the actual area is 45.

Thus, W(2W - 1) = 45

How would you solve this for W? Hint: Re=-arrange this into a quadratic equaton.

Answer 26

oh

Answer 27

Please do the work.

Answer 28

SO i factor 2w^2-w-45

Answer 29

i do ac method?

Answer 30

?

Answer 31

The (2W - 1) is in the place of L in the equation W*L=A

Answer 32

Again, the area is 45, and that 45 equals W(2W-1).

Multiply out: W(2W-1). Do that now, please.

Answer 33

What is W*W?
What is W*1?

Then, putting this together, what is W(W-1)?

Answer 34

@MathDude0000 do you remember how to do trinomials?

Answer 35

@MathDude0000: I'm glad to help you. However, I do expect your full attention. I undrstand that this problem has been difficult for you, but assure you it will become easier with practice.

I must now excuse myself from OpenStudy. I urge you to continue working on this problem, with Atilda.