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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