A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 9 meters, the new total area of the garden will be 169 square meters. Find the length of each side of the original garden.
• 9 m
• 13 m
• 2 m
• 4 m
Show how you got the answer - thanks.
each side of the new area of the garden = 13
since 13x13 = 169
(side x side = area of square)
so 13-9
=4m
Therefore, 4m should be the answer
( x + 9 ) ^ 2 = 169 Take the square root of both sides
x + 9 = 13 Subtract 9 from both sides
x + 9 - 9 = 13 - 9
x = 4
The length of the original garden = 4 m
Well, well, well! Let's solve this puzzle and find out the length of each side of the original garden.
So, we have a square flower garden and we know that when we increase each side of the original garden by 9 meters, the new total area becomes 169 square meters.
Let's call the length of each side of the original garden "x".
When we increase each side by 9 meters, we get a new length of "x + 9".
Now, we can create an equation to represent the problem. The equation for the area of a square is side length squared, so:
(x + 9)^2 = 169
Now, let's solve this equation.
Expanding the equation, we get:
x^2 + 18x + 81 = 169
Subtracting 169 from both sides, we have:
x^2 + 18x + 81 - 169 = 0
Simplifying further, we get:
x^2 + 18x - 88 = 0
Alright, let's factor this quadratic equation:
(x + 22)(x - 4) = 0
Oh ho ho! It seems we have two solutions: -22 and 4.
But hold your horses, my friend! A negative side length doesn't make sense. So, we discard -22.
Therefore, the length of each side of the original garden is 4 meters.
Now, go forth and enjoy your square flower garden, my friend!
To find the length of each side of the original garden, we can use the given information that the new total area of the garden, after it is expanded, is 169 square meters.
Let's denote the length of each side of the original garden as "x" meters. Since the garden is square, all sides are equal.
When each side of the original garden is increased by 9 meters, the new length of each side becomes (x + 9) meters.
To find the new total area of the garden, we can square the new length of each side: (x + 9)^2
According to the problem, this new total area is 169 square meters. So we have the equation:
(x + 9)^2 = 169
To solve for x, we can take the square root of both sides of the equation:
√(x + 9)^2 = √169
Simplifying this, we get:
x + 9 = 13
Now, we can isolate x by subtracting 9 from both sides of the equation:
x = 13 - 9
x = 4
Therefore, the length of each side of the original garden is 4 meters.
The correct answer is: 4 m