Answer:
Word Problems in mathematics are difficult to answer if you do not know how to translate the words in the problem into algebraic expressions and equations.
The first step in solving the problem is to entirely read the problem and understand it carefully. Then list the information on the problem, and set variables for each given.
Refer to the given problem.
The first given in the problem is the shape of the garden, that is a square. We know that by definition, a square has 4 equal sides, meaning all sides have equal lengths. Thus, we can let the variable "x" as the length of each side of the square garden.
The second given we should consider in the problem is the area of the square. We know that the area of a square is just the product of its length and width, but since the square has equal sides, then its area would be the square of its side. Thus we have "x²" as the representation of the area of the original square.
The problem says that if each side is increased by 4, then its area will be 144m². Translating the phrase "if each side is increased by 4" we get "x + 4" as the new length of its side.
The last given to consider is the measure of the new side which is 12m. Translating the phrase "the measure of its side after increasing is 12m" we get "x+4=12"
After listing the given in the problem, we define what the problem asks for, that is "to show the solution how we get 12m as the new length of the side".
By using the algebraic expressions we got from translating the phrases, we now begin to create equations and start to solve the problem.
Using the new length of the side and its new area, we get "(x+4)(x+4)=144"
By performing the indicated operation on the equation, we simplify first "(x+4)(x+4)". Just multiply the following expression thus getting . Then we equate it to 144, getting .
Simplifying again the equation, we transpose all the variables to the left and all the numbers to the right, we get " or simply .
The resulting equation is a quadratic equation, therefore we need to find the roots of the equation by using factoring, we get "x = 8 ; -16 "
Therefore, the original length of the side of the square garden is 8 meters
since "-16" is not a valid length.
So, if we add "4" to the original length of the side, we get or .
So now we know how we get 12m as the new length.
