Applying quadratic formula

Question

Lisa has a rectangular picture which is 23 inches long and 21 inches wide. She wants to build a wooden frame for the picture but she only has 357 in.² of wood available, how wide will the border be?

Answer 1

Let x = border width.

With the border, the total area is:

A = (21 + 2x)*(23 + 2x)

357 = (21 + 2x)*(23 + 2x)

357 = 483 + 42x + 46x + 4x^2

357 = 4x^2 + 88x + 483

4x^2 + 88x + 126 = 0

2x^2 + 44x + 63 = 0

x = [ -b +/- sqrt(b^2 -4ac)] / (2a) Use the quadratic formula

x = [-44 +/- sqrt(1936 - 504)] / (4)

x = [-44 +/- sqrt(1432) ] / (4) Ignore negative root

x = [-44 + 37.84 ] / (4)

x = -11 + 9.46

x = 1.54

The border width can be less than or equal to 1.5 inches.