Respuesta :
Answer: the dimensions are 10 and 29
Step-by-step explanation:
Let x represent the length of one square carpet.
Let y represent the length of the other square carpet.
Area of one square carpet = x^2
Area of the other square carpet = y^2
The sum of the areas of the carpet is 941 square feet. It means that
x^2 + y^2 = 941 - - - - - - - -1
The difference of the areas of the carpets is 741 square feet. It means that
x^2 - y^2 = 741 - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
2y^2 = 200
y^2 = 200/2 = 100
Taking square root of the left hand side and right hand side of the equation, it becomes
y = √100
y = 10
Substituting y = 10 into equation 1, it becomes
x^2 + 10^2 = 941
x^2 + 100 = 941
x^2 = 941 - 100 = 841
Taking square root of the left hand side and right hand side of the equation, it becomes
x = √841 = 29
