Asketch is drawn that is 6 inches by 9 inches. it is put in a frame of uniform width. if the area of the sketch is equal to the area of the frame what is the width of the frame?

The sketch has a surface area of (6 * 9 =) 45 square inch. If the frame has the same surface area as the sketch the total surface will be (2 * 45 =) 90 square inch. Knowing the frame has a uniform width we can write the following equation: (6 + f) * (9 + f) = 90 where f is the width of the frame. Now we solve for f: (6 + f) * (9 + f) = 54 + 9f + f*f + 6f = 90. 54 + 15f + f^2 = 90. By moving the 90 to the left we get the following formula which we can solve using the quadratic formula: 1f^2 + 15f - 36 = 0. D = b^2 - 4ac = 225 - 4 * 1 * -36 = 369. (-b +/- sqrt(D)) / 2a = (-15 +/- 19.21) / 2 = -17.1047 and 2.1047. The frame can only have a positive number for its width so f should be 2.1047. We can verify the solution by filling in our answer in our first equation: (6 + f) * (9 + f) = 90 (6 + 2.1047) * (9 + 2.1047) = 90.0003. So the correct answer is 2.1047 inch.