Question

At a local theater the trap door has an area of 84 square feet, and a has a whole number length and side measure. A co cert grand piano needed for a performance has a length of 8 feet, 10 inches and a width of 5 feet, 2 inches. what is the length and the width of the trap door? what is the perimeter of the trap door?

Answer 1

i. The length of the trap door is 12 feet, and its width is 7 feet.

ii. The perimeter of the trap door is 38 feet.

Explanation:

The area of the trap door = 84 square feet. But the dimension of the grand piano =
`8.10^(\\)` by
`5.2^(`.

For the piano to pass through the door conveniently, the width of the door should be wider than that of the piano. And its length the same. Given that the length and side measure of the door has to be a whole number, then;

The width of the door would be 7 feet, so that:

Area of the door = length × width

84 = l × 7

⇒ l = 12

The length of the trap door is 12 feet, and its width is 7 feet.

2. Since the traap door has a shape of a rectangle, thus:

perimeter of the trap door = 2 (length + width)

= 2 (12 + 7)

= 38 feet

The perimeter of the trap door is 38 feet.