Answer:
DF = 5 units
Explanation:
Given a figure showing right triangle DGF with sides DG = 3 and FG = 4, you want the length of hypotenuse DF.
Pythagorean theorem
The Pythagorean theorem can be used to find the distance between two points that are the ends of the hypotenuse of a right triangle. Where 'a' and 'b' are the side lengths of the triangle, the hypotenuse 'c' satisfies ...
c² = a² +b²
DF² = DG² +FG²
DF² = 3² +4² = 9 +16 = 25
DF = √25 = 5
The length of line segment DF is 5 units.
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Additional comment
The sides of this right triangle DGF are of lengths 3, 4, and 5. This set of numbers often shows up in algebra and geometry problems, so is worth remembering. Any triangle with sides in the ratio 3:4:5 will be a right triangle.