Question

A rectangular photograph measuring 11 cm by 4 cm is to be displayed in a card mount in a rectangular frame as shown below, with a border of constant width x cm. The owner wants the area of the mount (including the photo) to be 75cm^2.

Answer 1

The calculated width of the border is 0.92 cm

How to determine the width of the border

From the question, we have the following parameters that can be used in our computation:

Dimensions = 11 cm by 4 cm

Area of the mount (including the photo) = 75 squate cm

Width of the border = x

Using the above as a guide, we have the following:

Area of the mount (including the photo) = (2x + 11) * (2x + 4)

This gives

Area of the mount (including the photo) = 4x² + 22x + 8x + 44

Area = 4x² + 30x + 44

So, we have

4x² + 30x + 44 = 75

4x² + 30x - 31 = 0

Solving graphically, we have

x = 0.92

Hence, the width of the border is 0.92 cm