Question

1. a window was to be installed in a basement where a ductwork ran parallel with the outside wall. the window measured 32\ x 20\ (l x h) and was to rest 24\ from the top of the wall. how much of the window would be covered by ductwork if the duct measured 8\ high and 16\ wide? (assume that the top of the duct was at the same elevation as the top of the wall.)

Explanation:

Step1: Determine the overlapping width

The duct is 16" wide and the window is 32" wide. The overlapping width is limited by the width of the duct, so the overlapping width $w = 16$ inches.

Step2: Determine the overlapping height

The window is 20" high and is placed 24" from the top of the wall, and the duct is 8" high. Since the top - of the duct is at the same elevation as the top of the wall, the overlapping height $h$ is determined by the height of the duct. So $h = 8$ inches.

Step3: Calculate the covered area

The area $A$ of the part of the window covered by the ductwork is given by the product of the overlapping width and height. Using the formula $A=w\times h$.
$A = 16\times8=128$ square inches.

Answer:

128 square inches