A picture that measures 11 inches by 3 inches is placed in a frame of uniform width. If the area of the frame and picture together is 273 square inches, what is the width of the frame?

Answer 1

Let x be the width of the frame in inches.

The length of the picture and frame together is 11 + 2x, and the width of the picture and frame together is 3 + 2x.

The area of the picture is 11 x 3 = 33 square inches.

The area of the picture and frame together is 273 square inches, so:

(3 + 2x)(11 + 2x) = 33 + 273

33 + 8x + 22x + 4x^2 = 306

4x^2 + 30x - 273 = 0

Using the quadratic formula, we find:

x = (-30 ± sqrt(30^2 - 4(4)(-273))) / (2(4))

x = (-30 ± sqrt(10836)) / 8

We can discard the negative solution, so:

x = (-30 + sqrt(10836)) / 8

x ≈ 2.4

Therefore, the width of the frame is approximately 2.4 inches.

Answer 2

If the picture is 11 x 3 with a frame of uniform width around it, then the dimensions of the frame

are:

2x+11 by 2x + 3 (because there is a width on both sides of the picture for both dimensions.

That means (2x+11)(2x+3) = 273

4x²+28x+33=273

4x²+28x-260=0

x²+7x-60=0

(x-5)(x+12) = 0

Take it from there.