SOLUTION: 3. Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for both variables.
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Question 208615: 3. Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for both variables.
The perimeter of a rectangle is 48 cm. The length is 12 cm longer than the width. Find the dimensions.
Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Let l be the length and w be the width. We know that perimeter is 48 so in equations this would be l + w =48 so that will be our first equation. We also know that the length of is 12 cm longer than the width. In equations this would be l = 12+w, which is our second equation.
so our system is
l + w = 48
l = 12 + w
So since we have an expression for l we can use the substitution method and plug equation 2 into equation 1 and solve for width.
l + w = 48
12 + w + w = 48
12 + 2w = 48
2w = 36
w = 18 cm
so we know the width is 18 centimeters. Now we plug that back into equation 2 and find the length.
l = 12 + w
l = 12 + 18
l = 30 cm
so we know that the width is 18 centimeters and the length is 30 centimeters and checking that does give us a perimeter of 48 centimeters so that checks.
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