how do i find the area??

Question

If the length of a rectangular patch of farmland was increased by 30 percent, and the width decreased by 20 percent, what would be the percent increase in the area of the patch of land?
i do not want the answer i want how to work it out

i still don't understand when ever i multiply it it gives me 600

my answers are 4% 10% 25% 30% 50%

Answer 1

A = length * width
The new area is (1.30 * length)(0.80 * width)
Multiply these to see how the area changed.

Answer 2

The best way to think of it is by imagining the square farmland. The length is L and the width is W. We know that L times W equals the area, A. L x W = A

So, we use the same equation but just add the new details of the new farmland in. The length has been increased by 30 percent, so we find what 30 percent of L is and and add it to L. (*Don't forget that L actually is 1L)
1L + .30(1L) = the new length
1.3L = the new length

And we do the same for the width, but subtract 20 percent of W since it's decreasing.
1W - .20(1W) = the new width
.8W = the new width

So now, we multiply the new length and the new width to get the new area of farmland:
(1.3L) x (.8W) = Area of the new farmland
1.04LW = A

The original A = 1LW
The new A = 1.04LW

So, we now know that the new land has increased by .04 LW.

1.04LW - 1LW = .04LW

Lastly, we just need to figure out what percent .04LW is of the original LW. The equation for this is:

the increased amount = original amount times X

.04LW= LW(X) ...cancelling out the LW's, we get:
X = .04 ... if we convert this into percent
X = 4%

The answer is the farmland has increased by 4%

To better understand all this, it's easier if you plug in numbers. I used 5 for the length and 3 for the width.

5 x 3 = 15 (This is the original area)
[5 + .3(5)] x [3 - .2(3)] = A (This is the new area)
(6.5)(2.4) = 15.6 (This is the new area)
15.6 has increased .6 from the original area.
.6 = 15X
X = 0.04
X = 4%

There you go! Hope this helps

Answer 3

OK. Think... what's the formula for the area of a rectangle? Now we increase L by 30%, giving us L + .30L. Then we decrease W by 20%, or W - .2W. Now reformulate the area of the rectangle with the new L and W. Hold onto both formulae. Select a value for L and for W and plug them into each equation. Then take the smaller answer and subtract it from the greater answer. Divide that answer by 8. This gives you the percent increase in area. Do NOT listen to onetonkilla..Please.

Answer 4

Let A1 be the initial area of the land with length l and width w.
(1) A1=lw

Let A2 be the area after the specified adjustments are made. The dimensions are now:
length = (1+.3)l, width = (1-.2)w
Therefore:
(2) A2 =(1.3)(0.8)lw = 1.04lw = 1.04A1

The percent increase (I) is:

(3) I = (A2-A1) /A1 X 100%

Substitution of (1) and (2) into (3) gives the answer, which you asked me not to tell you.

Answer 5

Just do length times width, or 20x30= 60% pretty simple stuff once you figure out how to do formula.

Answer 6

ok, look at it this way-
L=length
w=width
x= multiplication
Area= (L(.3)+L) x (w(.2)+w)
hope this helps, by the way, make sure u multiply correctly