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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.
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, 30^{2} + 8^{2} = c^{2}; 900 + 64 = c^{2}; 964 = c^{2}; 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 ; 31.05^{2} + 122 = AB^{2}; 964 + 144 = AB^{2}; 1,108 = AB^{2}. 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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