Problema Solution
Suppose that the length of a rectangle is 3cm longer than twice the width and that the perimeter of the rectangle is 90cm.
a) Set up an equation for the perimeter involving only W, the width of the rectangle
b) Solve this linear equation algebraically to find the width of the rectangle. Find the length as well.
c) Using the same length as your answer in part (b), find a new perimeter if the new width is 5 less than one-half of the length Answer and Explain your work here.
Answer provided by our tutors
Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm. Set up an equation for the perimeter involving only W, the width of the rectangle. On The Question About The Rectangle Being 90 Centimeters, I Also Was Needing The Equation Algebraically To Find Length Of The Rectangle And The Width As Well?
Step 1. The perimeter P means adding up all the four sides of a rectangle.
Step 2. Let w be the width.
Step 3. Let 2w+3 be the length since the length is three cm longer than twice the width.
Step 4. Then, P=w+w+2w+3+2w+3=90.
Step 5. Solving yields the following steps
Subtract 6 from both sides of the equation
Divide by 6 to both sides of the equation
For , then and P=2(14+31)=90 which is a true statement.
Step 6. ANSWER: The width is 14 cm and the length is 31 cm.