A rectangle has a length 6 more than it’s width if the width is decreased by 2 and the length decreased by 4 the resulting has an area of 21 square units what is the length of the original rectangle what is ratio of the original rectangle area to the new rectangle area what is the perimeter of the new rectangle

Length of original rectangle is : x+6 = 5+6 = 11 units

ratio of the original rectangle area to the new rectangle area:  

perimeter of the new rectangle : 2(x+2+x-2) = 4x = 4(5) = 20 units

Step-by-step explanation:

Here we have , A rectangle has a length 6 more than it’s width if the width is decreased by 2 and the length decreased by 4 the resulting has an area of 21 square units what is the length of the original rectangle . We need to find what is ratio of the original rectangle area to the new rectangle area what is the perimeter of the new rectangle . Let's find out:

Initial parameters of rectangle are : Length = x+6 , width = x

width is decreased by 2 and the length decreased by 4  :

Length = x+6-4 = x+2 , width = x -2 , So area is :

⇒

⇒

⇒

⇒

⇒

So , Length of original rectangle is : x+6 = 5+6 = 11 units

ratio of the original rectangle area to the new rectangle area:

⇒

⇒

perimeter of the new rectangle : 2(x+2+x-2) = 4x = 4(5) = 20 units

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1