The length of the longest rod which can be kept inside a rectangular box is $27 c m$ . If the length and the breadth of the box are $23 c m$ and $10 c m$ respectively, find its height.

8 c m

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10 c m

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12 c m

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14 c m

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Solution

The correct option is D $10 c m$
Length of diagonal of bottom $=$ $\sqrt{{(23)}^{2} + {(10)}^{2}} = \sqrt{529 + 100} = \sqrt{629} c m$

Inner height $=$ $\sqrt{{(27)}^{2} - {(629)}^{2}} = \sqrt{729 - 629} = \sqrt{100} = 10 c m$

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The length of the longest rod which can be kept inside a rectangular box is 27cm. If the length and the breadth of the box are 23cm and 10cm respectively, find its height.

The correct option is D 10cmLength of diagonal of bottom = √(23)2+(10)2=√529+100=√629cmInner height = √(27)2−(629)2=√729−629=√100=10cm

The length of the longest rod which can be kept inside a rectangular box is $27 c m$ . If the length and the breadth of the box are $23 c m$ and $10 c m$ respectively, find its height.

The correct option is D $10 c m$
Length of diagonal of bottom $=$ $\sqrt{{(23)}^{2} + {(10)}^{2}} = \sqrt{529 + 100} = \sqrt{629} c m$

Inner height $=$ $\sqrt{{(27)}^{2} - {(629)}^{2}} = \sqrt{729 - 629} = \sqrt{100} = 10 c m$