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Answer:

15 is the missing length

The required length of the slanted area is 15 yards.

What are Pythagorean triplets?  

In a right-angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.

What is pythgorean theorem ?

Pythagorean theorem is defined as  to find the unknown side of a right-angled triangle. eg, Two sides of a right-angled triangle are given as 6 cm and 9 cm, then the hypotenuse (the third side) can be calculated using the formula, h² = p2²+ b²; where 'h' is the hypotenuse and 'p' and 'b' are the perpendicular and base.

Here,
let the hypotenuse be h
now applying the Pythagorean theorem,

h² = 9² + 12²
h²= 81 + 144
h² = 225
h = √225
h = 15


Thus, the required length of the slanted area is 15 yards.

Learn  more about Pythagorean triplets here:

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It is to be determined that the hypotenuse of the slanted area with perpendicular and base is 9 yards and 12 yards respectively.