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.

1) Equation to model the area of frame is

2) The equation is quadratic.

3) The width of picture fame is

Step-by-step explanation:

Given: Dimension of rectangular picture is 8 inches by 7 inches

           Area of picture frame is 34 inches²

Solving to find the dimension of picture frame.

Assuming that picture frame has uniform width of "x".

using the area of rectangle formula to solve.

Area of frame=

Using distributive property of multiplication

⇒

Subtracting both side by 34

⇒  (quadratic equation)

Taking GCF as 2

⇒

dividing both side by 2

⇒

Solving by using quadratic formula.

Formula:

∴ In the expression , we have a= 2, b= 15 and c= 11.

Now, subtituting the value in the formula.

=

=

Opening parenthesis.

=

=

∴ x=  

Hence; 1) Equation to model the area of frame is

2) The equation is quadratic.

3) The width of picture fame is

25% is the answer