Each side of a square is lengthened by 8 inches. The area of this new, larger square is 196 square inches. Find the length of a side of the original square.
Let's start with the square root of 196 = 14
I think you can take it from there.
To find the length of a side of the original square, we can follow these steps:
Step 1: Let's assume the length of a side of the original square is "x" inches.
Step 2: According to the problem, each side of the original square is lengthened by 8 inches. So, the length of a side of the larger square would be "x + 8" inches.
Step 3: The area of the larger square is given as 196 square inches. We can find the area of a square by squaring the length of its side. Therefore, the area of the larger square can be calculated as (x + 8)^2.
Step 4: According to the problem, the area of the larger square is 196 square inches. So, we can set up the equation: (x + 8)^2 = 196.
Step 5: Now, let's solve this equation to find the value of "x". Taking the square root of both sides, we get: x + 8 = √196.
Step 6: Simplifying further, we have: x + 8 = 14.
Step 7: Subtracting 8 from both sides, we get: x = 14 - 8.
Step 8: Simplifying, x = 6.
Therefore, the length of a side of the original square is 6 inches.