If the length of a rectangle is increased by 40% and its width is decreased by 40% what is the effect on the rectangles area ?

We want to see how some changes in the measures of a rectangle affect the area of the given rectangle.

We will see that the new area is 0.84 times the original area (meaning that the area decreases by 16%).

We will have.

First, we know that for a rectangle of length L and width W the area is given by:

A = L*W

Now, if we increase the length bt 40%, the new length will be:

L' = L +  (40%/100%)*L = L*1.4

And if the width is decreased by 40%, the new width will be:

W' = W - (40%/100%)*W = W*0.6

The new area is given by:

A' = L'*W' = (L*1.4)*(W*0.6) = (L*W)*(1.4*0.6) = 0.84*(L*W)

Where L*W is the area of the original rectangle, so we can write:

A' = 0.84*A

Meaning that the area decreased, the new area is 0.84 times the original area (we can actually see that the area decreased by 16%).

If you want to learn more, you can read:

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The area is multiplied by 0.84 (decreased 16%)

Step-by-step explanation:

The length is multiplied by (1 +0.40) = 1.4.

The width is multiplied by (1 -0.40) = 0.6

So, the new area is ...

A = (L·1.4)·(W·0.6) = LW·0.84

The original area was the product of the original length and width, so was LW. This means the new area is 0.84 times the original area.

0.84 = 1 - 0.16

so, another way to describe the change is to say the area decreased 16%.

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

step-by-step explanation:

answers available in this download

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