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Question
The hypotenuse of a right angled triangle is 5cm and the other two sides differ by 1cm . Find the lengths of the sides of the triangle
The hypotenuse of a right angled triangle is 5cm and the other two sides differ by 1cm . Find the lengths of the sides of the triangle
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Solution
Let one of the sides be x then another side is 1+ x
Applying Pythagoras theorem
(5)² = (x)² + (x + 1)²
25 = x² + x² + 2x + 1
25 = 2x² + 2x + 1
2x² + 2x - 24 = 0
x² + x - 12 = 0
x² + 4x - 3x - 12 = 0
x(x + 4) - 3(x + 4) = 0
(x - 3)(x + 4) = 0
x= 3 or x = -4
But length can't be negative.
So one of the side is 3 cm while the other is 4 cm
You can verify this too!
(3)² + (4)² = 9 + 16 = 25
Hypotenuse = √25 = 5 cm
Applying Pythagoras theorem
(5)² = (x)² + (x + 1)²
25 = x² + x² + 2x + 1
25 = 2x² + 2x + 1
2x² + 2x - 24 = 0
x² + x - 12 = 0
x² + 4x - 3x - 12 = 0
x(x + 4) - 3(x + 4) = 0
(x - 3)(x + 4) = 0
x= 3 or x = -4
But length can't be negative.
So one of the side is 3 cm while the other is 4 cm
You can verify this too!
(3)² + (4)² = 9 + 16 = 25
Hypotenuse = √25 = 5 cm
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