Mohání wishes to fit three rods together in the shape of a right triangle. If the hypotenus
is 2 cm longer than the base and 4 con longer than the shortest side, find the length
of the rods.
Answers
Let the altitude be x cm
Then
The hypotenuse is (x + 4) cm [hypotenuse is 4 cm longer than the altitude]
The base is ((x + 4) - 2) cm = (x + 2) cm [hypotenuse is 2 cm less than the base]
According to the right angle triangle law
Square of the hypotenuse = Sum of the squares of the other two sides.
=> (x + 4)^2 = x^2 + (x + 2)^2
=> x^2 + 16 + 8x = x^2 + x^2 + 4 +4x
=> x^2 + 16 + 8x = 2x^2 + 4 +4x
=> 2x^2 + 4 +4x - (x^2 + 16 + 8x) = 0
=> 2x^2 + 4 +4x - x^2 -16 -8x = 0
=> x^2 -4x -12 = 0
=> x^2 -6x +2x -12 = 0
=> x(x - 6) +2(x - 6) = 0
=> (x - 6) (x + 2) = 0
=> x - 6 = 0, x + 2 = 0
=> x = 6, -2
As a side cannot be negative; x = 6 cm =>Altitude is 6 cm.
The base = (x + 2) cm = (6 + 2) cm => 8 cm
The hypotenuse = (x + 4) cm => (6 + 4) cm => 10 cm
Therefore, the lengths of the rods are 6 cm, 8 cm and 10 cm.