Answer:
Let's represent each of the given scenarios using quadratic equations:
When the product of two numbers is 48, and their sum is 16.
Let the two numbers be x and y. We are given that the product of these numbers is 48, so we have:
xy = 48
We are also given that their sum is 16, so we have:
x + y = 16
When the product of two consecutive even integers is 288.
Let the first even integer be x. Then the next consecutive even integer is x + 2. We are given that the product of these integers is 288, so we have:
x(x + 2) = 288
When a rectangular field with an area of 120m² has its length 12m longer than the width.
Let the width of the rectangular field be x meters. Then the length of the field is x + 12 meters. We are given that the area of the field is 120 m², so we have:
Area = Length × Width
120 = (x + 12) × x
When the dimensions of a cube are reduced by 5cm on each side, and the new surface area becomes 48cm².
Let the original side length of the cube be x cm. When the dimensions are reduced by 5 cm, the new side length becomes (x - 5) cm. We are given that the new surface area is 48 cm², so we have:
New Surface Area = 48
2( (x - 5)² ) = 48
When the area of a floor is 864 sq. m., and its perimeter is 120 m.
Let the length of the floor be L meters, and the width be W meters. We are given that the area is 864 sq. m., so we have:
Area = L × W = 864
We are also given that the perimeter is 120 m, so we have:
Perimeter = 2L + 2W = 120
These are the quadratic equations representing each of the given scenarios. You can further simplify and solve these equations to find the values of the variables in each case.
Explanation: