Which of these cannot be the area of a right-angled triangle if the hypotenuse o

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Which of these cannot be the area of a right-angled triangle if the hypotenuse of the triangle is 13 m and one other side is 5 m?

Options:

A .

32.5 m^{2}

B .

78 m^{2}

C .

30 m^{2}

D .

60 m^{2}

Answer: Option A
:
A, B, and D

Let the triangle be ABC where AC = 13 m and BC = 5 m
Using Pythagoras theorem we can write,
$A B^{2} = A C^{2} - B C^{2}$

Therefore, $A B^{2} = 13^{2} - 5^{2} \Rightarrow A B = 12 m$
Area of triangle = $\frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times 5 \times 12 = 30 m^{2}$

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