SOLUTION: Hello and thank you for taking the time to help me with this. I have figured out the answer to my length and width. The solution I have is P=2(l+w)=2*(33+16)=98. I am not understa

Question 1162163: Hello and thank you for taking the time to help me with this.
I have figured out the answer to my length and width. The solution I have is P=2(l+w)=2*(33+16)=98. I am not understanding what I need to do to answer the remaining questions.
A rectangle has perimeter 98 cm and its length is 1 cm more than twice its width.

Find the dimensions of a rectangle given that its perimeter is 98 cm and its length is 1 cm more than twice its width.
Part a: How is P related to L and W? To measure the perimeter, you need to go down one length, across one width, back one length, and back one width. Write that as an equation for P in terms of L and W. This is your answer to part a.

Part b: You should continue to use the information given in the question. The length is 1 more than twice the width - write that as an equation for L in terms of W. This is your solution to part b.

Your equation from part a has 3 variables (P, L and W) and you'd like to reduce it to 2 variables. You're told that P=98. You can put that into your perimeter equation for P.

Now the perimeter equation has 2 variables (L and W) and you'd like to reduce it to 1 variable. Use your equation from part b to replace L.

Now the perimeter equation has only 1 variable (W) left!

Parts c and d: Solve the equation for W and use your answer to calculate L.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
P = 2L + 2W = 2 * (L + W)
P = 98, therefore:
98 = 2 * (L + W)
L = W + 1, therefore:
98 = 2 * (W + 1 + W)
combine like terms to get:
98 = 2 * (2 * W + 1) = 4 * W + 2
subtract 2 from both sides of the equation to get:
96 = 4 * W
solve for W to get:
W = 96/4 = 24
since L = W + 1, then L = 25
P = 2L + 2W = 2 * (L + W) = 2 * 49 = 98
this confirms the solution is correct.
we have the solution.
now to answer the questions in turn.
the questions are:

Find the dimensions of a rectangle given that its perimeter is 98 cm and its length is 1 cm more than twice its width.

Part a: How is P related to L and W? To measure the perimeter, you need to go down one length, across one width, back one length, and back one width. Write that as an equation for P in terms of L and W. This is your answer to part a.

P = 2 * L + 2 * W = 2 * (L + W)

Part b: You should continue to use the information given in the question. The length is 1 more than twice the width - write that as an equation for L in terms of W. This is your solution to part b.

L = W + 1

Your equation from part a has 3 variables (P, L and W) and you'd like to reduce it to 2 variables. You're told that P=98. You can put that into your perimeter equation for P.

Now the perimeter equation has 2 variables (L and W) and you'd like to reduce it to 1 variable. Use your equation from part b to replace L.

P = 2 * (L + W) becomes 98 = 2 * (W + 1 + W)
combine like terms to get:
98 = 2 * (2 * W + 1)
simplify to get:
98 = 4 * W + 2

Now the perimeter equation has only 1 variable (W) left!

Parts c and d: Solve the equation for W and use your answer to calculate L.

subtract 2 from both sides of the equation to get:
96 = 4 * W
divide both sides of the equation by 4 to get:
96/4 = W
solve for W to get:
W = 24
solve for L to get:
L = W + 1 = 25

your solution is P = 98 and L = 25 and W = 24

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