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In a right angled triangle given below, which of the following is the longest side?

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A B

A C

B C

All are equal

answer is B.

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Detailed Solution

We have been given

Δ A B C

with

∠ B = 90 °

and hypotenuse AC.
Question Image

We know that the sum of three angles of a triangle is

180 ° .

∠ A + ∠ B + ∠ C = 180 °

⇒ ∠ A + 90 ° + ∠ C = 180 ° ∵ ∠ B = 90 ° ⇒ ∠ A + ∠ C = 90 °

⇒ ∠ A + ∠ C = ∠ B ∵ ∠ B = 90 °

⇒ ∠ A < ∠ B ...... (1)

Similarly,

∠ C < ∠ B ....... (2)

For a triangle, the length of the opposite side of a larger angle is larger.

⇒ A C > B C ... 3

A C > A B ... 4

From equations (3) and (4), we have hypotenuse AC as the longest side of the right-angled triangle

Δ A B C .

Therefore, AC is the longest side.
So, option (2) is correct.

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