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.


(I just need help finding the length of the lines, then I can do it :3)
(Thank you!!)

Answer 1

square has all perimeter lines identical. to find the length of a side you can use a^2 = b^2 + c^2
24^2 = 576

as b and c are equal you can just divide 576 by 2 to get 288.
square root of 288 = 16.97 feet 

Answer 2

A unique square has a unique lengthed diagonal. For putting the molding around the perimeter of the roof, Shelton will need 67.9 feet of molding (approx)

How are side of a square and its diagonals are related?

Since a square has its adjacent sides perpendicular to each other, thus, drawing a diagonal gives us two right angled triangles, both congruent. Assuming that the length of the sides of a square = a units, then,

by using the Pythagoras theorem, we get the length of its diagonal as:

$D^2 = a^2 + a^2\\\\D = \sqrt{2a^2} = a\sqrt{2} \: \rm units$

(positive root as D is length of the diagonal and length is a non-negative quantity).

For the given case, it is already given that the roof is square, and its diagonal is of 24 ft length.

Thus, D = 24 ft

Supposing that its side is 'a' units, we get:

$D = a\sqrt{2}\\\\a = \dfrac{D}{\sqrt{2}} = \dfrac{24}{\sqrt{2}} = 12\sqrt{2} \: \rm feet$

Thus, its side is of $12\sqrt{2}$ feet.

Since perimeter of a closed figure is sum of its sides, and as there are four sides of a square, thus,

Perimeter of roof = $4 \times a = 4 \times 12\sqrt{2} = 48\sqrt{2} \approx 67.9 \: \rm feet$

Thus, For putting the molding around the perimeter of the roof, Shelton will need 67.9 feet of molding (approx)

Learn more about Pythagoras theorem here:

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