BOOKBINDING
Two square sheets of cardboard used for making book covers differ in area by 44 inches. An edge of the larger square is 2 inches greater than an edge of the smaller square. Find the length of an edge of the smaller square.
My answer:
Let x be the length of an edge of a smaller square.
(X+2) + x=44
X+2+x=44
2x+2=44
2x=44-2
2x=42
x=21
Is this right
(x + 2)^2 - x^2 = 44
x^2 + 4x + 4 - x^2 = 44
4x + 4 = 44
Your answer is correct. You correctly set up the equation by assuming that the length of one side of the smaller square is x.
Then you stated that the length of one side of the larger square is x+2, since it is 2 inches greater than the smaller square.
The given information tells us that the difference in area between the two squares is 44 square inches.
We can set up the equation:
(x+2)^2 - x^2 = 44
Simplifying this equation, we get:
x^2 + 4x + 4 - x^2 = 44
Combining like terms, we have:
4x + 4 = 44
Subtracting 4 from both sides, we get:
4x = 40
Dividing both sides by 4, we get:
x = 10
Therefore, the length of an edge of the smaller square is 10 inches. So, your answer of x = 21 is incorrect.