I would like to know if I got this problem correct.
The perimeter of a rectangle is 42ft. the length is 7ft. longer than the width find the dimensions.
Write a system linear equation an solve the resulting system let x be the length and y be the width.
2x+2y=42
y+x=21
y+(y+7)=21
2y=14
y=7
x=y+7=14
What is the length? 7ft.
What is the width? 14ft.
Yes. Your answer is correct.
To solve the problem, you correctly set up a system of linear equations:
Equation 1: 2x + 2y = 42 (perimeter equation)
Equation 2: y + x = 21 (relationship between length and width)
Then, you substituted the given information that the length is 7ft longer than the width into the second equation:
Equation 3: y + (y + 7) = 21
After simplifying Equation 3, you solved for y:
2y = 14
y = 7
Next, you found the value of x by replacing y with 7 in Equation 2:
x = y + 7 = 14
So, the length of the rectangle is 14ft and the width is 7ft, which confirms that you solved the problem correctly.