Mathematics
Grade10
Easy
Question
A rectangular patio has an area of 2x2 + 13x – 24 square feet. The patio is to be enlarged so that each dimension is 2 ft. greater than it was originally. What is the new area of the patio?
- 2x2 + 15x – 10
- 2x2 - 20x – 24
- x2 + 19x – 10
- 2x2 + 19x – 10
Hint:
Quadratic polynomial is a polynomial in which the highest degree monomial is of the second degree.
The correct answer is: 2x2 + 19x – 10
2x2 + 13x – 24
a = 2, b = 13, c = -24
ac = -48
Factors of -48 are 16 and -3.
16 + (-3) = 13
2x2 + 16x – 3x – 24 = 2x(x + 8) – 3(x + 8) = (2x – 3)(x + 8)
The dimensions of the patio are 2x – 3 ft. by x + 8 ft.
New dimensions are:
2x – 3 + 2 = 2x – 1 ft.
And x+8+2 = x + 10 ft.
So, new area = (x+10)(2x-1) = 2x² +19x -10.
Hence, the correct option is D.
Area of a rectangle = length × breadth sq. units.
