Answer:
1. 14.9 cm
2. 16.9 cm
4. 18.7 in
6. 50 m
Explanation:
The Pythagorean theorem relates the legs (a, b) and the hypotenuse (c) of a right triangle:
c² = a² +b²
If you want to know the hypotenuse, take the square root:
c = √(a² +b²)
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1.
In the given rectangular prism, length AC is the hypotenuse of right triangle ABC, which has legs AB=14 and BC=5 in units of centimeters. Then ...
AC = √(14² +5²) = √(196 +25) = √221 ≈ 14.9 . . . cm
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2.
Length AD is the hypotenuse of the right triangle with legs AC=√221 and CD=8 in units of cm. Then ...
AD = √((√221)² +8²) = √(221 +64) = √285 ≈ 16.9 . . . cm
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4.
The slant height (s) of the cone is the hypotenuse of the right triangle with legs r=5 and h=18 in units of inches. Then ...
s = √(5² +18²) = √(25 +324) = √349 ≈ 18.7 . . . inches
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6.
The slant height of the pyramid is the altitude of any of the triangular faces. As such, it is the hypotenuse of the right triangle whose legs are half the base dimension, 40 m, and the given height, 30 m. We recognize these numbers as multiples of the sides of a {3, 4, 5} triangle, so we know immediately the slant height is 50 meters.
s = √(40² +30²) = √2500 = 50 . . . meters