Problema Solution
1, the sides of a square are decreased by 3cm, the area is decreased by 81cm^2. What were the dimensions fo the original square?
2, One number is 8 less than another. Let x represent the larger number and use a rational expression to represent the sum of the reciprocals of the two numbers. help?
Answer provided by our tutors
1) There are two ways of solving this problem. One is to use two variables in two equations and use the variable "s" for the length of the sides and "a" for the area. The second, more efficient way is to use only one variable, which is "s" for side and "s^2" for area. I will use the second to solve the problem.
Let s = original length of the sides
s^2 = original area
s-3 = side decreased by 3cm
(s^2)-81=area decreased by 81cm^2
(s-3)^2=(s^2)-81
s^2-3s-3s+9=(s^2)-81
s^2-6s+9=(s^2)-81
s^2-s^2-6s=-81-9
-6s=-90
s=-90/-6
s=15cm
a=s^2=15^2=225cm^2
The original side is 15cm and the original area is 225cm^2
2)Same with the first, this can be solved either by using one variable or two. Let's use only one variable.
Let x=the larger number
x-8=the smaller number
(1/x)+(1/x-8)
This expression can be further simplified by getting the LCD, which is x(x-8) and evaluating...
(x-8)+x/x(x-8)
(2x-8)/x^2-8
The rational expression is (2x-8)/x^2-8.
There you go. Hope I helped!