A) \[\text{16 cm}\]
B) \[\text{18 cm}\]
C) \[\text{17 cm}\]
D) data insufficient.
Correct Answer: B
Solution :
| [b] Suppose hypotenuse of the triangle is c and other sides are a and b, obviously. |
| \[c=\sqrt{{{a}^{2}}+{{b}^{2}}}\] |
| We have, |
| \[a+b+c=40\] and \[\frac{1}{2}ab=40\Rightarrow ab=80\] |
| \[c=40-(a+b)\] and \[ab=80\] |
| \[{{(a+b)}^{2}}-2\times 40(a+b)+1600={{a}^{2}}+{{b}^{2}}\] |
| \[{{a}^{2}}+{{b}^{2}}+2\times 80-80(a+b)+1600={{a}^{2}}+{{b}^{2}}\] |
| \[80(a+b-2)=1600\] |
| \[a+b=22\] |
| \[c=40-(a+b)\] |
| \[=40-22=18\,cm\] |
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