Question

A 4-inch picture frame surrounds a picture which is 4 inches longer than it is wide, and the area of the frame is 192 in^2. Write an equation to determine the dimensions of the picture.

a) (4x + 4)(x) = 192
b) 4(x + 4) = 192
c) (4x + 4)(x + 4) = 192
d) 4(x) = 192

Answer 1

The equation to determine the dimensions of the picture is (4x + 4)(x + 4) = 192. To solve this equation, distribute and multiply the terms, subtract 192 from both sides, and solve the resulting quadratic equation.

Step-by-step explanation:

The equation to determine the dimensions of the picture is (4x + 4)(x + 4) = 192.

To solve this equation, you need to distribute and multiply the terms:

4x * x + 4 * x + 4x + 4 * 4 = 192

4x^2 + 8x + 16 = 192

Next, subtract 192 from both sides of the equation:

4x^2 + 8x - 176 = 0

Finally, solve the quadratic equation for x using factoring, the quadratic formula, or graphing.