Question

If the lengths of two sides of an obtuse angled triangle are 8 cm and 10 cm and the length of the third side (in cm) is also a natural number, what can be the
maximum length of the longest third side?
Enter your response (as an integer) using the virtual keyboard in the box provided below.

Answer 1

Answer:

If two sides are 8 and 15, then third side will have to be between (15-8) = 7 and (15+8) = 23.

When c is the longest side in obtuse triangle,

a2 + b2 < c2

If 15 is the longest side, then x can be 8, 9, 10, 11 or 12

If x is the longest side, then x can be 18, 19, 20, 21 or 22

Thus, 10 values of x are possible.

The correct option is B.

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Answer 2

Given: If the lengths of two sides of an obtuse angled triangle are 8 cm and 10 cm and the length of the third side (in cm) is also a natural number.

To find: The maximum length of the longest third side.

Solution:

In an obtuse-angled triangle, the length of the third side lies between two parameters. The first parameter is the difference between the other two sides and the second parameter is the sum of the other two sides. Hence, the parameters can be calculated as follows.

$10 - 8 = 2 cm$

$10 + 8 = 18$

Since the third side needs to be the longest, its length must be between 10 cm to 18 cm.

Therefore, the maximum length of the longest third side is 18 cm.