If the sides of a square are lenthened by 7 cm, the area becomes 121 cm^2. Find the length of a side of the original square
4cm
384cm square ...what is the length and with
To solve this problem, we can follow these steps:
Step 1: Let's assume the length of a side of the original square is "x" cm.
Step 2: If the sides of the square are lengthened by 7 cm, then the new length of each side becomes "x + 7" cm.
Step 3: The area of a square is calculated by multiplying the length of one side by itself. Therefore, the area of the square with the lengthened sides is (x + 7) cm * (x + 7) cm = (x + 7)^2 cm^2.
Step 4: Given that the area of the square with the lengthened sides is 121 cm^2, we can set up the equation: (x + 7)^2 = 121.
Step 5: We can solve this equation to find the value of x. Taking the square root of both sides gives us x + 7 = √121.
Step 6: √121 simplifies to 11, so we have x + 7 = 11.
Step 7: Subtracting 7 from both sides gives us x = 11 - 7.
Step 8: Simplifying further, we find x = 4.
Therefore, the length of each side of the original square is 4 cm.