The width of a rectangle is (5x-7). Find the polynomial equation reppresenting the area of the rectangle if its lenght is three more than four times as long as its width
L = 4 w + 3
A = L w = [ 4 (5x-7) + 3 ] (5x-7)
= [ 20 x - 28 + 3 ] (5x-7)
= (20x - 25)(5x+7)
= 5 (4x-5)(5x+7)
= 5 (20 x^2 +3 x -35)
= 100 x^2 + 15 x - 175
To find the polynomial equation representing the area of the rectangle, let's first determine the length of the rectangle.
Given that the length of the rectangle is three more than four times its width, we can express this as:
Length = 4(Width) + 3
Substituting the given width expression, (5x - 7), into the equation, we have:
Length = 4(5x - 7) + 3
Length = 20x - 28 + 3
Length = 20x - 25
Now that we have the length and width of the rectangle, we can find the area by multiplying the length and width together:
Area = Length × Width
Area = (20x - 25)(5x - 7)
To simplify the polynomial equation, we can use the distributive property:
Area = 20x(5x - 7) - 25(5x - 7)
= 100x^2 - 140x - 125x + 175
Combining like terms, we get:
Area = 100x^2 - 265x + 175
Therefore, the polynomial equation representing the area of the rectangle is 100x^2 - 265x + 175.