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?

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.

Step-by-step explanation:

The area of the trap door = 84 square feet. But the dimension of the grand piano = by .

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.

10010010001010010101001001010010100101010010101010010010101010110010001011010010010001

step-by-step explanation:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.