Mathematics
The hypotenuse of a right triangle is 25 cm. If out of the two legs, one is longer than the other by 5 cm, then the sum of the lengths of the legs is:
30 cm
35 cm
40 cm
45 cm
Answer
Let one leg = x cm and the other = (x + 5) cm
From figure,
AB = (x + 5) cm, BC = x cm and AC = 25 cm, ∠B = 90°
By Pythagoras theorem,
Hypotenuse2 = Perpendicular2 + Base2
In triangle ABC,
⇒ AC2 = AB2 + BC2
⇒ 252 = (x + 5)2 + x2
⇒ 625 = x2 + 25 + 10x + x2
⇒ 2x2 + 10x + 25 - 625 = 0
⇒ 2x2 + 10x - 600 = 0
⇒ 2(x2 + 5x - 300) = 0
⇒ x2 + 5x - 300 = 0
⇒ x2 - 15x + 20x - 300 = 0
⇒ x(x - 15) + 20(x - 15) = 0
⇒ (x + 20)(x - 15) = 0
⇒ x = -20 or x = 15
Since, length cannot be negative.
x = 15 cm.
Sum of the lengths = x + (x + 5) = 15 + (15 + 5) = 15 + 20 = 35 cm.
Hence, Option 2 is the correct option.
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