Question

Mack wrote the equation x² + 7x + 84 = x² + 13x + 30 to show that the area of a changed rectangle is 84 ft² greater than the area of the original rectangle. How did the rectangle change?

3 was added to each side.
7 was added to each side.
10 was added to each side.
13 was added to each side.
PLZZZZ HELP!!!1

Answer 1

3 was added to each side (K12)

Answer 2

Option A. 3 was added to each side is correct

Explanation:

First equation is given to be : x² +7x + 84

Area of the changed rectangle is 84 greater than the Area of original rectangle therefore the part of the equation which represents the Area of the rectangle = x² + 7x

= x(x + 7)

Length = x and breadth = x + 7

Now, the other equation is : x² + 13x + 30

⇒ x² + 3x + 10x + 30

⇒ (x+3)(x+10)

⇒ (x + 3)(x + 7 + 3)

Length = x + 3 and breadth = x + 10

Now, by comparing both the equations of the area it may be noted that each side is increased by 3

Hence, Option A. 3 was added to each side is correct