Question 228242
The length of a red rectangle is 15 cm more than its width w. A blue rectangle, which is 5 cm wider and 2 cm shorter than the red one, has perimeter 72 cm. Find the dimensions of each rectangle.


Step 1.  Perimeter P means adding up all 4 sides of a rectangle.


Step 2.  Let w be the width of the red rectangle


Step 3.  Let w+15 be the length of the red rectangle


Step 4.  Let w+5 be the width of the blue rectangle


Step 5.  Let w+15-2=w+13 be the length of the blue rectangle


Step 6.  Then for the blue rectangle, P=w+5+w+5+w+13+w+13=4w+36=72


Step 7.  Solving  4w+36=72 using the following steps


Subtract 36 from both sides of the equation


{{{4w+36-36=72-36}}}


{{{4w=36}}}


Divide by 4 to both sides of the equation


{{{4w/4=36/4}}}


{{{w=9}}} and {{{w+15=24}}} 


{{{w+5=14}}} and {{{w+13=22}}}  And {{{P=2(14+22)=72}}} which is a true statement


Step 5.  ANSWER:  For the red triangle the width is 9 cm and the length is 24 cm.  For the blue triangle, the width is 14 cm and the length is 22 cm.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J