| The base of a right prism is a right angled triangle whose sides are 5 cm, 12 cm and 13 cm. If the area of the total surface of the prism is \[360\,c{{m}^{2}},\]then its height (in cm) is |
A) 9
B) 11
C) 10
D) 12
Correct Answer: C
Solution :
| Total surface area of the prism \[=360\,c{{m}^{2}}\] |
| \[\Rightarrow \] Surface area of the prism + 2 (Area of the base) = 360 |
| \[\Rightarrow \]\[(5+12+13)\times h+2\,\,\left( \frac{1}{2}\times 5\times 12 \right)=360\] |
| \[\Rightarrow \] \[30h+60=360\,\,\,\Rightarrow \,\,\,30h=300\] |
| \[\Rightarrow \] \[h=10\,cm\] |
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