Mathematics
The hypotenuse of a right triangle is 6 m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.
Answer
Let the shortest side be x meters.
Hypotenuse = 2x + 6 meters
Third side = 2x + 6 - 2 = 2x + 4 meters.
Since, the sides are of a right triangle.
By pythagoras theorem,
⇒ (Hypotenuse)2 = (First Side)2 + (Second side)2
⇒ (2x + 6)2 = (x)2 + (2x + 4)2
⇒ 4x2 + 36 + 24x = x2 + 4x2 + 16 + 16x
⇒ 4x2 + 36 + 24x = 5x2 + 16 + 16x
⇒ 5x2 - 4x2 + 16x - 24x + 16 - 36 = 0
⇒ x2 - 8x - 20 = 0
⇒ x2 - 10x + 2x - 20 = 0
⇒ x(x - 10) + 2(x - 10) = 0
⇒ (x + 2)(x - 10) = 0
⇒ x = -2 or x = 10.
Since, side cannot be negative,
x ≠ -2.
Shortest side = 10 m
Hypotenuse = 2x + 6 = 2(10) + 6 = 26 m
Third side = 2x + 4 = 2(10) + 6 = 24 m.
Hence, sides of triangle = 10 m, 24 m and 26 m.
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