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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