Question

A square ceiling has a diagonal of 24 ft. Shelton wants to put molding around the perimeter of the ceiling.

How many feet of molding will he need?

Round to the nearest foot.

Enter your answer in the box.


_____ Ft.

Answer 1

Shelton needs 68 feet of molding.

68 feet

Explanation:

A square ceiling has a diagonal of 24 ft.

Shelton wants to put molding around the perimeter of the ceiling.

Let the side of the square of ceiling be x ft

We are given 24 is diagonal of this square.

Using pythagoreous theorem.

Sum of square of side of square is equal to square of diagonal.

`x^2+x^2=24^2`

`2x^2=576`

`x^2=288`

Taking square root both sides

`x=√(288)`

`x=16.97\approx 17`

Now, we find the perimeter of square.

P = 4x

P = 4(17)

P = 68 foot

Hence, Shelton needs 68 feet of molding.

Answer 2

The length of the side is half the length of the diagonal over square root 2:

24/2 = 12

Side length = 12√2 = 16.97 feet.

Perimeter is 4 times the length of one side:

Perimeter = 16.97 x 4 = 67.88 Round up to 68 feet.