If the sides of a square are lenthened by 7 cm, the area becomes 222 cm squared. Find the length of a side of the original square.
225 cm squared....sorry
A = s^2
Square root of 225 = 15
15-7 = ?
first, represent:
let x = the length of the original square
let x+7 = the length of the new square
since area of square is (length of side)^2:
A=s^2
225=(x+7)^2
225=x^2+14x+49 *transpose all terms to one side
x^2+14x-176=0
(x-8)(x+22)=0 *get only the positive since there is no negative length
therefore,
x=8 cm
so there,, =)
To solve this problem, we can use algebraic equations. Let's represent the length of a side of the original square as 'x'.
According to the given information, when the sides of the square are lengthened by 7 cm, the new side length becomes 'x + 7'.
The area of the original square is given by x^2, and the area of the square with lengthened sides is (x + 7)^2.
We know that the area of the square with lengthened sides is 222 cm^2. So we can set up the equation:
(x + 7)^2 = 222
To solve this equation, we can expand the square on the left side:
x^2 + 14x + 49 = 222
Next, we can rearrange the equation to isolate x by subtracting 222 from both sides:
x^2 + 14x + 49 - 222 = 0
Simplifying further:
x^2 + 14x - 173 = 0
Now, we need to solve this quadratic equation to find the value of x. We can do this by factoring, completing the square, or using the quadratic formula.
In this case, the quadratic equation does not factor easily. So, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 14, and c = -173. Plugging these values into the quadratic formula, we get:
x = (-14 ± √(14^2 - 4(1)(-173))) / (2(1))
Simplifying further:
x = (-14 ± √(196 + 692)) / 2
x = (-14 ± √888) / 2
Taking the square root of 888 gives us:
x = (-14 ± 29.8) / 2
Now we can calculate the two possible values of x:
x1 = (-14 + 29.8) / 2
x1 = 15.8 / 2
x1 = 7.9
x2 = (-14 - 29.8) / 2
x2 = -43.8 / 2
x2 = -21.9
Since the length of a side cannot be negative, we can disregard x2 = -21.9. Therefore, the length of a side of the original square is 7.9 cm.