Q. 16 A3.7( 3 Votes )
In ΔABC, if AB = (2a-1)cm. AC = 2 √2acm. And BC = (2a + 1)cm., then let us write the value of ∠BAC.
Let’s consider that the triangle is a right angled triangle,
By applying Pythagoras theorem we get,
(2a + 1)2 = (2√2a)2 + (2a-1)2
⇒ (2a)2 + 12 + 2×2a×1 = 4×2a + (2a)2 + 12 - 2×2a×1
⇒ 4a2 + 1 + 4a = 8a + 4a2 + 1 - 4a
⇒ 4a2 + 1 + 4a = 4a2 + 1 + 4a
Since, the sides of the triangle satisfy Pythagoras theorem, thus the triangle is a right angled triangle with angle opposite to hypotenuse as right angle.
H = 2a + 1
P = 2a-1
B = 2√2a
Thus, ∠BAC is a right angle with measure 90°.
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