Question

A photograph is 18 cm by 12 cm. It is to be surrounded by a frame of uniform width whose area is equal to that of the photograph. Find the width of the frame

Answer 1

Ok so the area of the frame is 18*12 = 216cm^2

Let’s suppose the width of the frame is x

The total area (painting and frame) is (2x+18)(2x+12) and this is equal to 432

4x^2 + 60x + 216 = 432

4x^2 + 60x - 216 = 0

x^2 + 15x - 54 = 0

(x+18)(x-3) = 0

Therefore x = {-18,3}
Since width of the frame has to be positive, the width has to be 3cm