Question

a room is 13 ft long and 8ft wide the length and width are both increased by the same number of feet if the new perimeter of the room is 53 1/2ft what is the length of the extension

Answer 1

5.75 ft
Find the perimeter, subtract it from the new perimeter, divide the result by 2

Answer 2

Answer: 5 3/4 feet

Explanation:

The original perimeter of the room is:

2(length + width) = 2(13 ft + 8 ft) = 42 ft

After the length and width are increased by "x" feet, the new perimeter becomes 53 1/2 ft.

So, we can write the equation:

2(length + x + width + x) = 53 1/2 ft

Simplifying the equation, we get:

2(length + width + 2x) = 53 1/2 ft

But we know that the original perimeter of the room was 42 ft, so:

2(length + width) = 42 ft

Substituting this into the above equation, we get:

42 ft + 2x = 53 1/2 ft

Subtracting 42 ft from both sides, we get:

2x = 11 1/2 ft

Dividing both sides by 2, we get:

x = 5 3/4 ft

Therefore, the length and width of the room were both increased by 5 3/4 feet