SOLUTION: The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height

Algebra ->  Rectangles -> SOLUTION: The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height      Log On


   

Question 480862: The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height.
Answer by nerdybill(7384) About Me  (Show Source):
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The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height.
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Draw a diagram, it'll help you see the solution.
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Begin by find the length of the diagonal on the bottom:
Let d = diagonal
then
d^2 = 8^2 + 12^2
d^2 = 64 + 144
d^2 = 208
d = sqrt(208)
d = 14.222 cm
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Now, we can find the inner height:
Let h = inner height
then
h^2 + 14.222^2 = 17^2
h^2 + 208 = 289
h^2 = 81
h = 9 cm