| What is the area of a right angled triangle? |
| I. The perimeter of the triangle is 30 cm. |
| II. The ratio between the base and the height of the triangle is 5: 12. |
| III. The area of the triangle is equal to the area of a rectangle of length 10 cm. |
A) II and III together are necessary
B) I and II together are necessary
C) Out of I, II and III any two together are necessary
D) All three, I, II and III together are necessary
E) None of the above
Correct Answer: B
Solution :
| II. Hypotenuse \[=\sqrt{{{5}^{2}}+{{12}^{2}}}\] |
| \[=\sqrt{25+144}=\sqrt{169}=13\] |
| \[\therefore \] Base: Height: Hypotenuses 5 : 12 : 13 |
| I. Base+ Height + Hypotenuses 30 cm |
| \[\therefore \] \[Base=\frac{5}{5+12+13}\times 30=5\,cm\] |
| \[Height=\frac{12}{5+12+13}\times 30=12\,cm\] |
| Area \[=\frac{1}{2}\times \]Base \[\times \]Height \[=\frac{1}{2}\times 5\times 12=30\,c{{m}^{2}}\] |
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