If the sides of a square are lengthened by 8cm the area becomes 169^2. Find the length of a side of the original square.
I am getting 34.25cm
If you typed the question correctly, then the answer is obvious
(x+8)^2 = 169^2
then x+8 = 169
and x=161
The square root of 169 is 13, which is the lengthened measure of each side. Subtract 8 from 13 to find the original length of each side.
You must have a typo. I think you mean the area is 169 cm^2
(S+8)^2 = 169
for which I get 5 cm
However if it really is as you wrote it
then
(S+8)2 = 28561
S + 8 = 169
S = 161
TYPO 169cm^2 My apologies.
To solve this problem, let's break it down into steps:
Step 1: Let's assume that the length of one side of the original square is x cm.
Step 2: If the length of each side of the square is increased by 8 cm, then the new length of one side of the square is (x + 8) cm.
Step 3: The new area of the square is given as 169^2 square cm.
Step 4: We can set up an equation using the formula for the area of a square:
(x + 8)^2 = 169^2
Step 5: Simplify the equation:
x^2 + 16x + 64 = 169^2
Step 6: Subtract 169^2 from both sides:
x^2 + 16x + 64 - 169^2 = 0
Step 7: Solve the quadratic equation by factoring or using the quadratic formula. In this case, it is easier to use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 1, b = 16, and c = 64 - 169^2.
x = (-16 ± √(16^2 - 4(1)(64 - 169^2))) / (2 * 1)
Step 8: Calculate the value of x using a calculator:
x ≈ -194 or x ≈ 178
Since the length of a side cannot be negative, we discard the negative value, leaving us with x ≈ 178 cm.
Therefore, the length of a side of the original square is approximately 178 cm, not 34.25 cm.