Determine the length of the diagonal, Mathematics

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A box is 30 cm long, 8 cm wide and 12 cm high. Determine the length of the diagonal AB ? Round to the nearest tenth.

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a. 34.5 cm

b. 32.1 cm

c. 35.2 cm

d. 33.3 cm

d. This problem needs two steps. First, determine the diagonal of the base of the box. Second, using this value, determine the length of the diagonal AB . To determine the diagonal of the base, use 30 cm as a leg of a right triangle, 8 cm as the second leg, and answer for the hypotenuse. Using the Pythagorean theorem, 302 + 82 = c2; 900 + 64 = c2; 964 = c2; c = 31.05. Now consider this newly get value as a leg of a right triangle, 12 cm as the second leg, and simplfy for the hypotenuse, A B ; 31.052 + 122 = AB2; 964 + 144 = AB2; 1,108 = AB2. AB = 33.3. If you select a, you used 30 and 12 as the calculation of the legs. If you select b, you answer the ?rst triangle correctly; however, you used 8 as the measure of one leg of the second triangle, which is incorrect.


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