The length of a rectangle is 3 cm more than twice its width. The perimeter of the rectangle is 96 cm. What are the dimensions of the rectangle

Question

I cannot figure out how to solve this problem for me to study tonight for my test at sc

Answer 1

Hello Jade, 

The formula for the perimeter is as follows: P = 2(L) + 2(W) 

 

 

Let x = the width
Let 2x + 3 = the length    <------The length of a rectangle is 3 cm more than twice its width


Therefore: 

P = 2(L) + 2(W)   <------You are given the perimeter as 96 cm in the problem


96 = 2 (2x +3) + 2 (x)   <------We are merely substituting values here, okay? 

Now solve for x by simplifying. 

96 = 4x + 6 + 2x   <------We used the distributive law of math for first term and then simplified 

Now solve for x by adding like terms. 

96 = 6x + 6 

Now subtract 6 from both sides. 

90 = 6x
15= x 

Always proof your work. The question is when you substitute 15 for x in the original equation, does it = 96

96 = 2(15) + 2 (2*15 +3) 
96 = 30 + 2 (33)
96 = 30 +66 
96 =96 

We have proven our work. Your answer will be in centimeters.

Hope this helps. Good luck on your test and have a great day in school.