Question

Mrs Alivia’s bathroom is in the shape of a rectangle with a width of 6 feet. Her kitchen is in the shape of a rectangle with a width of 10.75 feet. The perimeter of Mrs Avilia’s bathroom is 29 feet. Which statements about the length of Mrs. Avila’s bathroom are true.

1. The length of the bathroom is equal to its width.

2. The equation 2(x+6)=29 can be used to find the length of the bathroom, x.

3. The legend of the bathroom is 11.5 feet.

4. The equation 2x+6=29 can be used to find the length of bathroom, x.

5. The length of the bathroom is 8.5 feet.

Answer 1

1. The length of the bathroom is equal to its width. FALSE

2. Equation 2(x+6)=29 can be used to find the length of the bathroom, x.

TRUE

3. The legend of the bathroom is 11.5 feet. FALSE

4. The equation 2 x+6=29 can be used to find the length of bathroom, x.

FALSE

5. The length of the bathroom is 8.5 feet. TRUE

Explanation:

Here, given:

The width of the bathroom = 6 feet

The width of the kitchen = 10.75 ft

The perimeter of the bathroom = 29 feet

Let us assume the length of the bathroom = k units

PERIMETER OF A RECTANGLE = 2 ( LENGTH + WIDTH)

Now, for the Mrs Avila's bathroom

29 feet = 2 (k + 6)

⇒ 29 = 2k + 12

or, 2 k = 29 - 12 = 17

⇒ k = 17/2 = 8.5 feet

So, the length of the bathroom = 8.5 units

Now, let us consider the given statements:

1. The length of the bathroom is equal to its width. FALSE

As here, Length= 8.5 units and width = 6 units

2. Equation 2(x+6)=29 can be used to find the length of the bathroom, x.

TRUE

3. The legend of the bathroom is 11.5 feet.

FALSE, the length of the bathroom is 8.5 units.

4. The equation 2 x+6=29 can be used to find the length of bathroom, x.

FALSE, the correct equation that can be used is 2x + 12 = 29

5. The length of the bathroom is 8.5 feet.

TRUE