Length of a side on a square is 5cm longer than the side of another square. the total area is 193cm. what is length of original?
area of first = x^2
area of 2nd = (x+5)^2
x^2 + x^2 + 10x + 25 = 193
2x^2 + 10x - 168 = 0
x^2 + 5x - 84 = 0
(x - 7)(x + 12) = 0
x = 7 or x = -12 , which would be a silly square
the first square is 7 by 7
the second is 12 by 12
check: 49 + 144 = 193 , yeahhh!
To find the length of the original square, we can set up a system of equations using the given information.
Let's call the length of the side of the original square "x" cm.
The length of the side of the other square would then be "x + 5" cm.
The formula to calculate the area of a square is: Area = side length * side length.
According to the given information, the total area of both squares is 193 cm^2. Therefore, we can create the equation:
x^2 + (x + 5)^2 = 193
Now, we can solve this equation to find the value of x, which represents the length of the original square:
x^2 + (x + 5)(x + 5) = 193
x^2 + (x^2 + 10x + 25) = 193
2x^2 + 10x + 25 = 193
2x^2 + 10x - 168 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 2, b = 10, and c = -168.
Plugging these values into the equation, we have:
x = (-10 ± √(10^2 - 4 * 2 * -168)) / (2 * 2)
x = (-10 ± √(100 + 1344)) / 4
x = (-10 ± √1444) / 4
x = (-10 ± 38) / 4
Now we have two possible values for x:
1) x = (-10 + 38) / 4 = 28 / 4 = 7
2) x = (-10 - 38) / 4 = -48 / 4 = -12
Since the length of the side cannot be negative, we discard the second solution.
Therefore, the length of the original square is 7 cm.