what is the maximum length and width of the house?

Question

 House is built on a lot 70 ft wide by 100 ft deep. the shorter side of the lot faces the street. The house must be 25 ft from the street, and 20 ft from the back lot line and 10 ft from each side lot line. What is the maximum length and width of the house. 

Answer 1

 

It's always best to draw a diagram to visualize geometric word problems.  After drawing a rectangle where the shorter sides are found at the top/bottom and the longer sides are at the right/left, label your rectangle with the given information:  Draw new lines inside of your rectangle marked an estimated 10 feet from the right and 10 feet from the left.  At the top, draw a new line an estimated 20 ft down from your original line.  At the bottom, draw a line an estimated 25 feet up from your original line.  Subtract 20 feet (10+10) from the original width of 70 to get 50.  Then subtract 45 feet (20 + 25) from your original depth of 100 to get 55.  

 

Make sure you re-read the question to be sure of the answer it seeks....it asks for the dimensions, not the area, so your answers are a maximum width of 50 and a maximum of 55 for depth.