SOLUTION: I need help with this problem: A rectangle is 7 times as long as it is wide. Its area is 1400cm^2. Find the dimensions of the rectangle in simplest radical form. I have been w

Algebra ->  Radicals -> SOLUTION: I need help with this problem: A rectangle is 7 times as long as it is wide. Its area is 1400cm^2. Find the dimensions of the rectangle in simplest radical form. I have been w      Log On


   

Question 194682This question is from textbook Florida Algebra 1
: I need help with this problem: A rectangle is 7 times as long as it is wide. Its area is 1400cm^2. Find the dimensions of the rectangle in simplest radical form.
I have been working on this problem for 30 minutes straight, and I can't find the way to work it out. I tried to use this equaion to solve the problem (length=7w): 1400=+2%287w%29+%2A+2w
I didn't work. Please help me. This question is from textbook Florida Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure how you got what you have, but I think you're confusing the area and perimeter formulas.

Since "A rectangle is 7 times as long as it is wide", this means that L=7W. Also, because "Its area is 1400cm^2", we know that A=1400


Recall, the area of a rectangle is A=LW


A=LW Start with the area of a rectangle formula


1400=7W%2AW Plug in L=7W and A=1400


1400=7W%5E2 Multiply


1400%2F7=W%5E2 Divide both sides by 7


200=W%5E2 Reduce


W%5E2=200 Rearrange the equation


W=sqrt%28200%29 Take the square root of both sides. Note: we're only considering the positive square root.


W=sqrt%28100%2A2%29 Factor 200 to get 100*2


W=sqrt%28100%29%2Asqrt%282%29 Break up the square root.


W=10%2Asqrt%282%29 Take the square root of 100 to get 10


L=7W Go back to the first equation


L=7%2A10%2Asqrt%282%29 Plug in W=10%2Asqrt%282%29


L=70%2Asqrt%282%29 Multiply



So the length is 70%2Asqrt%282%29 cm and the width is 10%2Asqrt%282%29 cm