Question

A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame? 4x + 12 8x + 24

Answer 1

The expression for the area of frame is 4x² + 24x + 35

What is Area of rectangle?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.

Here, Old length of photograph = 5 inch

          Old width of photograph = 7 inch

Now, length of new photograph = (5 + 2x) inch

        width of new photograph = (7 + 2x) inch

Now, Area of frame with new dimension = Length X breadth

                                                                     = (5+2x) X (7+2x)

                                                                     = 5(7+2x) + 2x(7+2x)

                                                                    = 35 + 10x + 14x + 4x²

                                                                    = 4x² + 24x + 35

Thus, the expression for the area of frame is 4x² + 24x + 35.

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