The area of a tiled kitchen floor is represented by the expression 4x2 + 24x + 27, where x represents the length of a single tile. The length, l, of the floor is 9 feet more than twice the length of a tile, x.
Which expression represents the width of the kitchen in terms of x?
Answers
Answer:
[4x² + 24x + 27]/[2x+9]
Step-by-step explanation:
Let
x--------> represents the length of a single tile
L-------> the length of the floor
W------> the width of the floor
A--------> area of a tiled kitchen floor
we know that
A=W*L
A=4x² + 24x + 27
so
W*L=4x² + 24x + 27---------> equation 1
L=2x+9------> equation 2
substitute equation 2 in equation 1
W*[2x+9]=4x² + 24x + 27
W=[4x² + 24x + 27]/[2x+9]
therefore
the answer is
the expression that represents the width of the kitchen in terms of x is
W=[4x² + 24x + 27]/[2x+9]
Answer:
2x + 3.
Step-by-step explanation:
We know that area = length • width. The area is also represented by 4x2 + 24x + 27.
We can factor this polynomial as (2x + 9)(2x + 3):
4x2 + 24x + 27
4x2 + 6x + 18x + 27
2x(2x + 3) + 9(2x + 3)
(2x + 9)(2x + 3)
Since the length of the kitchen is 9 feet more than twice an unknown, x, the length can be represented by 2x + 9.
This means the width must be 2x + 3.