A) Less than 8 cm
B) Greater than or equal to 8 cm but less then or equal to 22 cm
C) Less than 22 cm
D) Greater than 22 cm
Correct Answer: B
Solution :
[b] Let the shortest side be x cm. |
Then, by given condition, second length \[=x+3\,\,cm\] |
Third length \[=2xcm\] |
Also given, total length \[=91\] |
Hence, sum of all the three lengths should be less than or equal to 91 |
\[\Rightarrow x+x+3+2x\le 91\Rightarrow 4x+3\le 91\] |
Subtracting (-3) to teach tern, |
\[-3+4x+3\le 91-3\] |
\[\Rightarrow 4x\le 88\Rightarrow \frac{4x}{4}\le \frac{88}{4}\Rightarrow x\le \frac{88}{4}\] |
\[\Rightarrow x\le 22cm\] ? (i) |
Again, given that Third length \[\ge \] second length \[+5\] |
\[\Rightarrow 2x\ge (x+3)+5\Rightarrow 2x\ge x+(3+5)\] |
Transferring the term x to L.H.S., |
\[2x-x\ge 8\Rightarrow x\ge 8\] ? (ii) |
From equations (i) and (ii) length of shortest board should be greater than or equal to 8 but less than or equal to 22, i.e., \[8\le x\le 22.\] |
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