sivakavi wishes to fit three rods together in the shape of right triangle. the hypotenuse is to be in 2cm longer than the base and 4cm longer than the altitude. what should be the length of rods
Answers
Answer:
Step-by-step explanation:
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
Hypothenuse=10cm
Base=10-2=8cm
Altitude=10-4=6cm
Length of rods=10,8and 6cm.
