The length of a rectangle is 2m more than the width. The area is 15 sq m. Find the length and the width.?

Question

I know the answer but not how to get the answer.

how did u get 5 and 3?

L: 2*W
W: W
W(2*W), 2W + W squared
I don't know what to do after that.

Thanx (all of u). I've been tryting to figure that out for an hour.

Answer 1

To solve for any algebraic word problem, what you need to do is assign a variable to your standard of comparison. What are all the unknowns being compared to, in this word problem? "The length of a rectangle is 2m more than the width" shows that it is the width that is being compared to. So let's let w be the variable we used.

Let w = width of the rectangle.
Since the length is 2 more than the width,
w + 2 = length of rectangle.

Note the area of a rectangle is giving by the following formula:

A = (length) times (width)

But, we're given A to be 15 square meters. We also have a length and a width expressed as w. So,

15 = (w + 2) (w)

Expand the right hand side

15 = w^2 + 2w

Move the 15 to the right hand side.

0 = w^2 + 2w - 15

Now, factor.

0 = (w + 5) (w - 3)

This gives us an answer of w = -5 or w = 3.
However, the width of a rectangle can never be negative, so we discard the negative solution w = -5.

That means w = 3.
Since the length is w + 2, then the length is 3 + 2 = 5

So the length of the rectangle is 5 and the width is 3.

Answer 2

Rewrite: 1. L = 2 + w and 2. W = w
Area is 15 > Area formula is A = L * W

First:
15 = L * W
15 = (2 + w)(w)
15 = 2w + w^2
15 - 15 = 2w + w^2 - 15
0 = w^2 + 2w - 15

Second: factor the equation:

0 = (w + 5)(w - 3)

0 = w + 5
0 - 5 = w + 5 - 5
-5 = w; w = -5

0 = w - 3
0 + 3 = w - 3 + 3
3 = w; w = 3

Third: you exclude -5 because, you can't use a negative number. (3) is the number we replace with "w" in both equations:

1. L = 2 + w
L = 2 + 3
L = 5 meters

2. w = 3 meters

Answer 3

Length = Width +2

Width is the same

Lenght x width = 15 so

(Width + 2) x Width = 15

Width^2 + 2(Width) = 15

Width^2 + 2(Width) - 15 = 0 factorise

(w+5)(w-3)

Since the length cannot be a negative it must be 3m long

Length = Area/Width

= 15/3

= 5m

So: Length = 5m

Width = 3m

Answer 4

The equation for the portion of a rectangle is below: A = LW for that reason, L = (x + 6) and W = (x - 6). so which you get: A = LW A = (x + 6)(x - 6) A = x^2 - 36 108 = x^2 - 36 one hundred forty four = x^2 12 = x Now positioned that x cost into your unique parenthetic words: L = (x + 6) = (12 + 6) = 18 and W = (x - 6) = (12 - 6) = 6

Answer 5

Let width = x
Therefore, length = x + 2
Area = length * width = x(x+2) = x^2 + 2x = 15
x^2 +2x - 15 = 0
Factoring:
(x+5) (x-3) = 0
So, the width is: x = -5 or x = +3
When width = -5, length = -3 (e.g. x +2)
When width = +3, length = +5 (e.g. x +2)
Both values give you an area of 15 m^2

Note: The negative values reflect the same rectangle drawn in the 3rd quadrant of a Cartesian graph.

Answer 6

A=15=w(w+2)=w^2+2w
w^2+2w-15=0
(w+5)(w-3)=0 w must be >0 so
w-3=0
w=3m
l=w+2=3+2=5m
w=3m, l=5m
check 3*5=15m^2

Answer 7

(lenght = width + 2
(lenght x width = 15

So,
(2 + w) x w = 15
w² +2w - 15 = 0
delta = 2² - 4.1.-15
delta = 4 + 60
delta = 64

w = (-2 +/-\/64) : 2
w' = (-2 + 8) : 2 = 3
w" = (-2 - 8) : 2 = -5

lenght = width + 2
lenght = 3 + 2 = 5m
L x w =
5 x W = 15
w = 15 : 5
w = 3m
Answer: lenght, 5m and width, 3m.
<>>

Answer 8

the length is 5m, and the width is 3m. use the equation:
length x width=area
2x * x=15
solve for x=5
x=length of rectangle
subtract 2=width of rectangle

Answer 9

use 2 equations and 2 unknowns:
L= W+2
L*W=15

Solve for one

Answer 10

I too could come up with the answer, but have forgotten how to show the method. I found a rather complicated explation at algebrahelp.com.

http://www.algebrahelp.com/calculators/equation/