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A rectangle has perimeter 140 cm and its length is 1 cm more than twice its width. Find the dimensions of a rectangle given that its perimeter is 140 cm and its length is 1 cm more than twice its width. Set up your solution using the variables L for the length, W for the width, and P for the perimeter. Part a: Using the definition of perimeter, write an equation for P in terms of L and W. Part b: Using the relationship given in the problem statement, write an equation for L in terms of W. Solve the equations from parts a and b. Part c: The length is 47 O cm.

A rectangle has perimeter 140 cm and its length is 1 cm more than twice its width. Find the dimensions of a rectangle given that its perimeter is 140 cm and its length is 1 cm more than twice its width. Set up your solution using the variables L for the length, W for the width, and P for the perimeter. Part a: Using the definition of perimeter, write an equation for P in terms of L and W. Part b: Using the relationship given in the problem statement, write an equation for L in terms of W. Solve the equations from parts a and b. Part c: The length is 47 O cm.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.8: Rate-time-distance Problems
Problem 1OE
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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 = 140. 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 I variable (W) left! Parts c and d: Solve the equation for W and use your answer to calculate L.
Transcribed Image Text: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 = 140. 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 I variable (W) left! Parts c and d: Solve the equation for W and use your answer to calculate L.
A rectangle has perimeter 140 cm and its length is 1 cm more than twice its width. Find the dimensions of a rectangle given that its perimeter is 140 cm and its length is 1 cm more than twice its width. Set up your solution using the variables L for the length, W for the width, and P for the perimeter. Part a: Using the definition of perimeter, write an equation for P in terms of L and W. Part b: Using the relationship given in the problem statement, write an equation for L in terms of W. Solve the equations from parts a and b. Part c: The length is 47 Ocm.
Transcribed Image Text:A rectangle has perimeter 140 cm and its length is 1 cm more than twice its width. Find the dimensions of a rectangle given that its perimeter is 140 cm and its length is 1 cm more than twice its width. Set up your solution using the variables L for the length, W for the width, and P for the perimeter. Part a: Using the definition of perimeter, write an equation for P in terms of L and W. Part b: Using the relationship given in the problem statement, write an equation for L in terms of W. Solve the equations from parts a and b. Part c: The length is 47 Ocm.
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The perimeter of rectangle= 2L+W.

where, L is length of rectangle and W is width of rectangle.

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