Binomial squares and cubes

Question

A square-shaped painting is circled by a frame with a width of 4.0cm and an area of 544cm^2. Calculate the area of the painting.

Answer 1

This is a standard word problem in Algebra 1. I recommend that you learn how to use your textbook; I can guarantee there is an example problem just like this. It also never hurts to draw a square with a 4 cm frame. You learn that, if the painting is of length s, the painting + frame is of length s + 2*4 (frame on both sides of painting means multiply width of frame by 2). Thus, the painting + frame is of length s + 8.

The area of the frame is the area of the painting + frame - the area of the painting. Thus, the area of the frame is (s+8)^2 - s^2 = s^2 + 16s + 64 - s^2 = 16s + 64

16s + 64 = 544

16s = 480

s = 480/16

s = 30

The area of the painting is s^2 = 30^2 = 900

Note: if you created a really good drawing, you could see that the area of the frame is 4 * 4s (the four sides are each of width 4), plus the 4 corners of area 4 * 4^2, and adding these gives you 16s + 64. The standard way to arrive at the 16s + 64, though, is subtracting as above.