Step 1: Apply Pythagoras' Theorem: In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Step 2: Calculate the squares of the lengths of each side of triangle A:
( 5^2 = 25 \)
( 13^2 = 169 \)
( 12^2 = 144 \)
Step 3: Check if Pythagoras' Theorem holds true for the triangle by applying the formula:
( 144 + 25 = 169 \)
( 144 + 169 = 313 \)
Step 4: Since 313 is not equal to 169, which is the square of the hypotenuse, the triangle is not right-angled.
Conclusion: The triangle is not drawn accurately because the lengths of the sides do not satisfy Pythagoras' Theorem, which dictates that the square of the hypotenuse must be equal to the sum of the squares of the other two sides in a right-angled triangle.
