A frame x inches wide is shown around a 12 inch by 18 inch rectangular picture. The area of the framed picture can be represented by the expression (2x+12)(2x+

Question

A frame x inches wide is shown around a 12 inch by 18 inch rectangular picture. The area of the framed picture can be represented by the expression (2x+12)(2x+18). What is the width of the frame if the area of the framed picture is 391 square inches?

 

A. 2 1/2 inches.

B. 3 1/2 inches.

C. 12 1/2 inches.

D. 17 1/2 inches. 

Answer 1

We know that the area 391 needs to equal the expression. So we have the equation 391 = (2x + 12)(2x + 18).

Let's simplify and solve this equation.

391 = (2x)(2x) + (2x)(18) + (2x)(12) + (12)(18)

391 = 4x² + 36x + 24x + 216

391 = 4x² + 60x + 216

391 - 391 = 4x² + 60x + 216 - 391

0 = 4x² + 60x - 175

0 = 4(x² + 15 - ¹⁷⁵/₄)

0 = 4(x + ³⁵/₂)(x - ⁵/₂)

So x can equal either -³⁵/₂ or ⁵/₂. Since a measurement cannot be negative, x can only be ⁵/₂ or 2½.