Question

A 5-inch by 8-inch photograph was enlarged to make a poster, as shown. If the dimensions of the poster are left parenthesis, x, squared, minus, 6, right parenthesis(x
2
−6) by left parenthesis, x, squared, plus, 12, right parenthesis(x
2
+12) inches, what is the area of the poster?

Answer 1

Because the photo was enlarged proportionally, (x^2 − 6)/(x^2 + 12) = 5/8.
Solve: 8(x^2 − 6) = 5(x^2 + 12) → 8x^2 − 48 = 5x^2 + 60 → 3x^2 = 108 → x^2 = 36.

Dimensions: 36 − 6 = 30 in and 36 + 12 = 48 in.
Area = 30 × 48 = 1440 square inches.