Question

One edge of a painting is 6 in. longer than the shorter edge. The picture has a 2-in.-wide frame.

Part A
Which quadratic function represents the total area of the picture and frame?
Part B
What is the total area of the framed picture if its shorter edge is 8 inches long?
Enter your answer in the box.

Answer 1

Part A). (L² + 14L + 40) Square inches

Part B). 216 square inches

Explanation:

From the figure attached,

Length of the shorter edge of the painting = L in.

Length of the longer edge of the painting = (L + 6) in.

Part -A)

Length of the shorter edge of the painting plus frame = (L + 4) in.

Length of the longer edge of the painting plus frame = (L + 6 + 4)

= (L + 10) in.

Total area of the picture and frame = (Shorter edge)×(longer edge)

A = (L + 4)(L + 10)

A = L(L + 10) + 4(L + 10)

A = L² + 10L + 4L + 40

A = (L² + 14L + 40) Square inches

Part B)

Total area of the framed picture if L = 8 inches

Area = (8)² + 14(8) + 40

= 64 + 112 + 40

= 216 square inches

Therefore, area of the framed picture is 216 square inches.