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QuestionFind the length yy of a room's floor if its width is y−5y - 5 and the perimeter is 4y+14y + 1 meters. Show your work.

Studdy Solution

STEP 1

Assumptions1. The length of the room's floor is yy meters. . The width of the room's floor is y−5y -5 meters.
3. The perimeter of the room's floor is (4y+1)(4y +1) meters.
4. The perimeter of a rectangle (which we assume the room's floor to be) is given by the formula ×(length+width) \times (length + width).

STEP 2

First, we need to set up the equation using the formula for the perimeter of a rectangle.
Perimeter=2×(Length+Width)Perimeter =2 \times (Length + Width)

STEP 3

Now, plug in the given values for the length, width, and perimeter to set up the equation.
y+1=2×(y+(y−5))y +1 =2 \times (y + (y -5))

STEP 4

implify the equation by distributing the2 on the right side of the equation.
4y+1=2y+2y−104y +1 =2y +2y -10

STEP 5

Combine like terms on the right side of the equation.
4y+1=4y−104y +1 =4y -10

STEP 6

Subtract 4y4y from both sides of the equation to isolate the constant terms.
1=−101 = -10

STEP 7

This is a contradiction since1 is not equal to -10. Therefore, there is no solution for yy that would satisfy the given conditions.
The length of the room's floor cannot be determined from the given conditions.

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