A welder wants to weld three rods together in the shape of a right angle triangle the hypotenuse is to be to be longer than the peace and formative longer than its altitude find the length of the roads requires
Answers
Let the Altitude of a right triangle be x Given:Hypotenuse of a right triangle is 4 cm longer than the Altitude, then
hypotenuse is (x + 4) cm
Given: Hypotenuse is 2 cm longer than the base,then
Hypotenuse= base + 2
x+4 = base + 2
x + 4 -2 = base
x +2 = base
Base = (x + 2) cm
According to Pythagoras theorem: H² = P² +B²
(x + 4)² = x² + (x + 2)²
x²+ 16 + 8x = x² + x² + 4 +4x
[(a+b)²= a² +2ab +b²]
x² + 16 + 8x = 2x² + 4 +4x
2x² + 4 +4x - x² - 16 - 8x = 0
x² - 4x -12 = 0
x² -6x +2x -12 = 0 [by Middle term splitting]
x(x - 6) +2(x - 6) = 0
(x - 6) (x + 2) = 0
x - 6 = 0 or x + 2 = 0
x = 6 or x= -2
side cannot be negative ,so x = 6 cm Altitude (x) = 6 cm.
Base = (x + 2) cm = (6 + 2) cm = 8 cm
hypotenuse = (x + 4) cm = (6 + 4) cm = 10 cm
Hence,the lengths of the rods are 6 cm, 8 cm and 10 cm.