Question

A rectangular picture measures 6 inches by 8 inches. Charlie wants to build a wooden frame for the picture so that the framed picture takes up a maximum area of 100 square inches on his wall. The pieces of wood that he used to build the frame all have the same width.

write an equation or inequality that could be used to determine the maximum width of the pieces of wood for the frame Charlie could create. Explain how your equation or inequality models the situation.

Solve the equation or inequality to determine the maximum width of the pieces of wood used for the frame to the nearest tenth of an inch.

Answer 1

To determine the maximum width of the wooden pieces used for the frame, we can write & solve an equation based on the dimensions of the picture and the maximum area of 100 square inches.

Step-by-step explanation:

To determine the maximum width of the pieces of wood Charlie could use for the frame, we need to consider the dimensions of the picture and the maximum area of 100 square inches. Let's assume the width of each wooden piece is 'x' inches. We can write the equation:

(6 + 2x) * (8 + 2x) = 100

This equation represents the area of the framed picture, which should not exceed 100 square inches. Solving this equation will give us the maximum width of the wooden pieces used for the frame. By multiplying the brackets and rearranging the equation, we get:

4x^2 + 28x + 38 = 0

Solving this quadratic equation will give us the value of 'x' which represents the maximum width of the wooden pieces used for the frame, to the nearest tenth of an inch.

Answer 2

6×8×2 would be 100 inches