the ratio of length to width in a rectangle is 2:3. find the length of the rectangle when the area is 150 sq. in.

Question

be sure to indicate if a solution is to be rejected based on the contextual situation. 

Answer 1

width = 2x

length = 3x

 

2x(3x) = 150

6x²  = 150

x² = 25

x = ±5

 

Measurement is only positive.

 

Width is 10 in and length is 15 in.

Answer 2

L:W <==> 2:3

 

this means length divided by width is equal to 2 divided by 3

 

and this is how you turn that in to mathematical equation L/W = 2/3

 

which means L = 2W/3 (or W = 3L/2 but we will just use use L for substitution. either one would work equally)

 

we also know L times W (LW) = 150, which is the value of the area

 

Now substitute 2W/3 in place of L and you should see that we get

 

w(2W/3)=150 <==> (2/3)W^2= 150 <==> 2W^2 = 450 <==> W^2 = 225 W= 15 ==> L = 10

 

It would be a good practice for you to try the same problem substituting L instead of W

 

hope this helps