Question

Nicky wants to surround a 25 in. by 16 in. painting with a frame that is w inches wide. Which quadratic function represents the combined area A of the picture and the frame?

A. A(w) = 4w2 + 32w + 400

B. A(w) = 4w2 + 42w + 400

C. A(w) = 4w2 + 64w + 400

D. A(w) = 4w2 + 82w + 400

Answer 1

Option "D" is the correct answer to the following question.

Explanation:

Given:

Length of painting = 25 inch

Height of painting = 16 inch

Width of frame = w inch

Find:

Area of Picture with frame

Computation:

New length of painting = 25 + w + w

New length of painting = 25 + 2w inch

New height of painting = 16 + w + w

New height of painting = 16 + 2w

Area = l x b

So,

Area of Picture with frame = [25 + 2w][16 + 2w]

Area of Picture with frame = 400 + 50w + 32w + 4w²

Area of Picture with frame = 4w² + 82w + 400