Question

Alistair has a rectangular picture measuring 8 inches by 7 inches. He makes a frame for the picture, shown by the shaded area in the diagram. The area of the frame is 34 square inches, and the width of the frame is x inches. Use this information to complete the activity.
1.Using the given information, write an equation to model the area of the frame.
2.
Which type of equation did you write to model the given scenario, linear or quadratic?
3.Use the equation you created in part A to find the width of the picture frame

Answer 1

You are given a rectangular picture measuring 8 inches by 7 inches. Also, Alistair wants this to be framed and that the total area is 34 square inches. The width of the frame is x inches. To solve the dimension of the frame with value of x we have:

We have to assume that x here will be equal to all sides of the frame and so, using the area of the rectangle, we can model the equation like this:
A = LW (where A is the area, L is the length and W is the width)
36 = (8 - x)(7 - x)
36 = 56 - 8x - 7x + x²
x² - 15x +20 = 0 → model of our equation and in quadratic form

x² - 15x + 20 = 0
using a calculator, x = 1.48 inches

3.Use the equation you created in part A to find the width of the picture frame