Using the Pythagorean Theorem, the lengths are:
CX = 12 units
BD = 13 units
EF = 5 units.
What is the Pythagorean Theorem?
Given that in a right triangle, we have c as the hypotenuse (longest side), and a and b as the lengths of the other smaller legs, the Pythagorean Theorem states that: c = √(a² + b²).
We are given the following:
CD = 49 ft
AB = XY = 25 ft
PG = PF = GH = 4 ft
EG = 7 ft
CX = DY
AX = BY = 5 ft
CX = 1/2(CD - XY)
Substitute
CX = 1/2(49 - 25)
CX = 1/2(24)
CX = 12 units
DY = 12 units
Use the Pythagorean Theorem to find BD:
BD = √(BY² + DY²).
Substitute
BD = √(5² + 12²)
BD = 13 units
Use the Pythagorean Theorem to find EF:
EF = √(GH² + EP²)
EP = EG - PG = 7 - 4 = 3
GH = 4
Substitute the values into EF = √(GH² + EP²):
EF = √(4² + 3²)
EF = 5 units.
Thus, applying the Pythagorean Theorem, the lengths are:
CX = 12 units
BD = 13 units
EF = 5 units.
Learn more about the Pythagorean Theorem on:
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