Question

In a right angle triangle ,the hypotenuse is 10 cm more than the shortest side. If third side is 6 CM less than the hypotenuse, find the sides of the right angle triangle​

​

Answer 1

let shortest side x cm

hypo. = (x + 10) cm

third side = x + 10 - 6 = ( x + 4) cm

by PGT ,

a

Answer 2

Let the shortest side be x then hypotenuse = x + 10 and the third side = x + 10 -6 = x + 4
From pythagoras theorem
AB^2 + BC^ 2 = AC^2 (where AB = shortest side BC= third side and AC = hypotenuse)
so
(x)^2 + (x + 4)^2 = (x + 10)^2
x^2 + x^2 + 8x + 16 = x^2 + 20x + 100
2x^2 +8x + 16 = x^2 + 20x + 100
x^2 - 12x -84 = 0
(x - 6 )^2 = 120
(x - 6) = 2root 30
x = 6 + 2 root 30
thus the shortest side = x = 6+ 2root 30
The third side = x + 4 = 10 + 2root 30
The hypotenuse = x + 10 = 16 + 2root 30