Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.
The perimeter of a rectangle is 72m. If the width were doubled and the length were increasd by 9m, then the perimeter would be 114m. What are the dimentions?
2L+2W=72
2(2W) + 2(L+9)=114
check that.
Does this mean that the dimentions are 72 and 114 or do you take it father to find what w & l are which I think might be w=12 and l=24. does that sound right?
Of course you have to find width w, and length L.
I would go back and check W=12, L=24 in the original equations. If they check, you are home bound.
To translate the problem into a pair of linear equations, we can start by assigning variables to the dimensions of the rectangle. Let's say the width is represented by 'w' and the length is represented by 'l'.
According to the problem, the perimeter of a rectangle is 72m, which can be written as:
2(w + l) = 72
Next, it states that if the width were doubled and the length were increased by 9m, then the perimeter would be 114m. That can be expressed as:
2(2w + (l + 9)) = 114
Now, we have two linear equations:
1) 2(w + l) = 72
2) 2(2w + (l + 9)) = 114
To solve these equations, we can use either elimination or substitution. Let's use substitution.
From equation 1, we can isolate one variable in terms of the other. Let's isolate 'w':
w = 36 - l/2
Now substitute this value of 'w' into equation 2:
2(2(36 - l/2) + (l + 9)) = 114
Simplify the equation:
2(72 - l + l + 9) = 114
2(81) = 114
162 = 114
This equation is not true, which means there is no solution that satisfies both equations simultaneously. Therefore, there are no valid dimensions for the rectangle given the information provided in the problem.