Question

A photographer had to change the size of his cover photo. He increased the length by 30% and decreased the width by 10%. By what percent was the area of the final photo changed?

Answer 1

The percent change in the area of the final photo is 17%.

Step-by-step explanation:

To find the percent change in area, we need to calculate the change in area and divide it by the original area.

Let's say the original length of the cover photo is 'L' units and the original width is 'W' units. The original area is then given by 'A = L * W'.

The photographer increased the length by 30%, which means the new length is '1.3L'. The width was decreased by 10%, which means the new width is '0.9W'.

The new area is given by 'A_new = (1.3L) * (0.9W) = 1.17LW' units.

The change in area is 'A_new - A = 1.17LW - LW = 0.17LW' units.

To find the percent change, we divide the change in area by the original area and multiply by 100:

Percent change = (0.17LW / LW) * 100 = 17%.

Answer 2

• 17%

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Let the dimensions be x and y.

The area is:

• A = xy

When sides have changed we get:

• x + 30% = x + 0.3x = 1.3x
• y - 10% = y - 0.1y = 0.9y

The new area is:

• A = 1.3x * 0.9y = 1.17xy

The difference in areas is:

• 1.17xy - xy = 0.17xy

It represents 17% increase.