A photographer has to change the size of his cover photo. He increase the length by 30% and decrease the width by 10%.. By what percent was the area of the final photo changed

1 answer

To solve the problem, we can use the formula:

Final Area = (1 + Percent Increase/100) x (1 - Percent Decrease/100) x Original Area

Let's say the original length and width of the photo were L and W, respectively, so the original area was:

Original Area = L x W

After increasing the length by 30%, the new length becomes:

New Length = L + 0.3L = 1.3L

After decreasing the width by 10%, the new width becomes:

New Width = W - 0.1W = 0.9W

So the final area becomes:

Final Area = 1.3L x 0.9W = 1.17LW

The percent change in area can be calculated as:

Percent Change in Area = ((Final Area - Original Area) / Original Area) x 100%

Substituting the values, we get:

Percent Change in Area = ((1.17LW - LW) / LW) x 100%
Percent Change in Area = (0.17LW / LW) x 100%
Percent Change in Area = 17%

Therefore, the area of the final photo changed by 17%.