Q:

The perimeter of a rectangle is 110 meters and the length is 25 meters longer than the width. find the dimensions of the rectangle. let x= the length and y= the width. the corresponding modeling system is {2x+2y=110x−y=25. solve the system graphically.

Accepted Solution

A:
------------------------------------------------
Define x and y:
------------------------------------------------
Length = x
Width = y

------------------------------------------------
Construct the two equations:
------------------------------------------------
The perimeter is 110:
 2x + 2y = 110

The Length is 25m longer than the width:
x = y + 25

------------------------------------------------
Solve x and y:
------------------------------------------------
2x + 2y = 110 ---------------- (1)
x = y + 25 ---------------------(2)

Substitute (2) into (1):

2x + 2y = 110
2( y + 25) + 2y = 110
2y + 50 + 2y = 110
4y + 50 = 110
4y = 110 - 50
4y - 60
y = 15m

------------------------------------------------
Substitute y=15 into equation 1:
------------------------------------------------
x = y + 25
x = 15 + 25
x = 40m

------------------------------------------------
Find Length and Width:
------------------------------------------------
Length = x = 40m
Width = y = 15m

------------------------------------------------
Answer: Length = 40m , Width = 15m
------------------------------------------------