Question

Katie Ward is building a children's playhouse. She wants each window to have an area of 315 square inches for adequate air. For eye appeal, she wants each window to be six inches higher than wide. What are the dimensions of the window

Answer 1

Let x is height of window and y is width of window, then area of window is xy=315. And height is 6 inches bigger than width. x=y+6. Plug this value into first equation:
(y+6)y=315 -> y^2+6y-316=0, which has roots 15 and -21. Width should be positive, so y=15, so x=15+6=21.
Answer: height is 21 inches, width is 15 inches.