the perimeter of the rectangular foundation of a new house is 190 ft. find the dimensions of the foundation if its length is 25 ft shorter than three times its width

Answer 1

Rectangle = 4 sides, with 2 sides equal to X and 2 sides equal to Y, where Y and X can be the same value (ie square)

Perimeter of rectangle = 2X+2Y

Step 1: 190ft = 2X + 2Y

The length is 25ft shorter than three times its width

Let X be length and Y be width

Step 2: X = 3Y-25

Step 3: 190ft = 2(3Y-25) +2Y

Step 4: 190ft = 6Y-50+2Y

Step 5: 190ft =8Y-50

Solve Step 5 for Y, then insert answer into Y in Step 2 and solve for X.

An example worked all the way through:

Step 1: 310ft = 2X + 2Y

Step 2: X = 3Y-25

Step 3: 310ft = 2(3Y-25) +2Y

Step 4: 310ft = 6Y-50+2Y

Step 5: 310ft =8Y-50

Step 5a: 360=8Y

Step 5b: 45 =Y

Step 2a: X=3(45)-25

Step2b: X=110

Check:

______110____

|____________| 45

|____________|

^45 110

220+90=310