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Answer:
hypotenuse = 13.0 cm
Step-by-step explanation:
Given the dimensions of a right triangle whose legs have measures of 13 cm and 1 cm, we can use the Pythagorean Theorem to find the measure of the triangle's hypotenuse.
The Pythagorean Theorem states that the squared measure of a right triangle's hypotenuse is equal to the sum of the squared lengths of its legs. In other words:
Pythagorean Theorem: c² = a² + b²
Let c = hypotenuse
a = Leg₁ = 1 cm
b = Leg₂ = 13 cm
Substitute these values into the given formula to find the measure of the hypotenuse, c:
c² = a² + b²
c² = ( 1 )² + (13)²
c² = 1 + 169
c² = 170
Next, take the square root of c² and 170 to isolate c:
[tex]\displaystyle\mathsf{\sqrt{c^2}\:=\:\sqrt{170}}[/tex]
c = 13.04 or 13.0 cm
Therefore, the length of the hypotenuse is 13.0 cm.