The area of the portrait is 1,914 in2. The width is w inches wide, and the length is 8 inches less than twice the width. Find both the length and width of the portrait.

Answer 1

Since the width of the portrait is represented by the variable w, we can write the following expression to represent the length: 2w - 8

Then area is calculated by multiplying the length by the width. Here that would be:

A = length • width

1914 = (2w - 8) • w

1914 = 2w² -8w

This can be solved for w using factoring as follows:

1914 = 2w² -8w

1914 - 1914 = 2w² -8w - 1914

0 = 2w² -8w- 1914

0 = 2 (w² -4w- 957)

Factor (w² -4w- 957): 0 = 2(w -33) (w +29)

Since the width can't be a negative number, w would be 33 inches.

The length would be 2w - 8 OR 2•33 -8 = 66 - 8 = 58 inches

To verify the area:

A = 33 • 58 = 1914 inches ²